Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following...

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Name: ___________________________ Geometry Period _______ Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones! Please note: You may have random material checks in class Some days you will have additional handouts to support your understanding of the learning goals in that lesson. Keep these in a folder and bring to class every day. All homework for part one of this unit is in this booklet. Answer keys will be posted as usual for each daily lesson on our website

Transcript of Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following...

Page 1: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Name: ___________________________

Geometry Period _______

Unit 11: Solid Geometry

In this unit you must bring the following materials with you to class every day:

Calculator Pencil

This Booklet

A device

Headphones!

Please note:

You may have random material checks in class

Some days you will have additional handouts to support your understanding of

the learning goals in that lesson. Keep these in a folder and bring to class every

day.

All homework for part one of this unit is in this booklet.

Answer keys will be posted as usual for each daily lesson on our website

Page 2: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Solid Figures Formed by Translations

Leanning goal: How are solid figures formed through translations, and what are the properties of these solids?

Class Discussion:

Imagine this! You stand inside a hula hoop, which is dipped in bubble solution. Lift the hula hoop straight

up. Can you sketch the shape that the bubble will take? Do you know what this is called? What objects

do you know that take this shape?

Think-Pair-Share

What type of transformation is shown here? What are the important aspects/ properties of this transformation? Make connections! How does this relate to the class discussion? Google Sketch Up! Thinking in 3-D...Circles

Sketch the figure formed when a circle is "pushed" into 3 dimensions. Vocab Alert! Important Terms Below! What does the resulting solid look like? Base: Base View: Lateral Face: Lateral View:

11-1 Notes

Page 3: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

All about Cylinders! A cylinder is...

A 3-D Object. Two circular bases that are ____________ and ______________. Lateral faces are ______________. Can be formed when a circle is translated or “Pushed” into 3-D.

Other Important Properties:

Like a prism, but the bases are NOT polygons. Cross Sections The 2D shape that appears when you cut/slice a 3D solid with a plane: Two Types!

Parallel to the base (same shape as base view)

Perpendicular to the base ( same shape as lateral view)

Back to Google Sketch Up! Thinking in 3-D... Polygons

Let’s sketch some other shapes we could push into 3D!

What does the resulting solid look like?

BASE VIEW (cross Sect. to base) Lateral View( Cross sect. to the base)

Page 4: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

All about Prisms

A prism is...

A 3D solid Formed by translating a polygon. Two polygonal bases that are ____________ and _____________.

Other Important Properties

Prisms are names by their _________________. Lateral faces are always ___________________ except for the ________. All their faces are ______. Lateral Edges (the lines formed when the faces meet) are always ___________ and ____________. The number of lateral faces corresponds to the number of ___________ the base has.

Back to Google Sketch Up! Thinking in 3-D... Sketch the figure formed when the area of the square is "pulled" into 3 dimensions:

What does the resulting solid look like?

BASE VIEW (cross Sect. to base) Lateral View( Cross sect. to the base)

Cross sections!

What is the cross section parallel to the base?

What is the cross section perpendicular to the base?

Page 5: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

As a class! When we "pushed" a square into 3-D, we were using the concept of translations from our transformations unit. What transformation(s) do you think are required to create the solid below from the "pre-image" of the square base?

All about Pyramids

A pyramid is...

A 3D solid Formed by a ____________and a ___________.

Other Important Properties:

One base that is a polygon. Named by the base polygon. Lateral edges are congruent. Lateral faces are Isosceles triangles.

Page 6: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Practice

Applying our Knowledge 1. Name each of the solids below. Draw the base and lateral views and name the cross sections.

Base View: What 2D shape is the cross section parallel to the base?

Base View: What 2D shape is the cross section parallel to the base?

Base View: What 2D shape is the cross section parallel to the base?

Lateral View: What 2D shape is the cross section that is perpendicular to the base?

Lateral View: What 2D shape is the cross section that is perpendicular to the base?

Lateral View: What 2D shape is the cross section that is perpendicular to the base?

2. What appears to be a square piece of fabric is laid out on the ground and the corners are hammered in place. A pole is placed under the fabric and used to raise a shelter. What is the base view? What is the lateral view?

3. a) A redwood tree grows for 400 years before it is tragically cut down to make paper. For transportation, the tree is

sliced. What are the possible shapes the tree could take?

#3 continued on next page…

Page 7: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

b) Once the tree has been processed into paper, your geometry teacher uses it to make her copies for class. She stacks all her copies in a single pile. What solids could be formed by the copies? 4.

5.

6. For the following, sketch and name the solid that will match with the given cross section.

Page 8: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

11-1 Homework

Directions: Answer the following questions to the best of your ability. Show all work.

1) What types of solids are formed by just translations?

2) Draw the base and lateral view for each figure.

3) What is the name of the following solid object? How could you form this solid using transformations?

4) The radius of the circle on the bottom is 10 cm. What is the area of the base of this cylinder to the nearest 10th?

Base Lateral Base Lateral

Base

Page 9: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

5) The following cross sections were taken from a 3D solid. Figure 1 represents the cross section perpendicular to the

base, and figure 2 represents the cross section parallel to the base.

What is the name of the solid that formed these cross sections?

6) Based on what we’ve studied about prisms, identify two edges that are parallel and explain why.

7) A straw is placed into a rectangular box that is 3 inches by 4 inches by 8 inches, as shown in the accompanying

diagram. If the straw fits exactly into the box diagonally from the bottom left front corner to the top right back

corner, how long is the straw, to the nearest tenth of an inch?

8) Regents Review Questions!

Page 10: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Figures Formed by Rotations

Today’s Goal: How are solid figures formed through rotations, and what are the properties?

Let’s Help Math-Hoo out of a jam! Imagine this... You have a rectangular flag attached to a flagpole.

The wind blows so that the flag rotates all the way around the flagpole.

What figure would the "path" of the flag create?

Think about it! Yesterday we looked at solids formed by translations

*Which solids do you think might be formed by a rotation?

**What do each of these have in common?

Math-Hoo’s Problem Thinking in 3-D... Sketch the 2 dimensional polygon that was rotated:

*Solid Diagram:

*Views:

Base View: Lateral View:

*Cross Sections:

Parallel To Base: Perpendicular to Base:

11-2 Notes

Page 11: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Google Sketch Up!

Thinking in 3-D...Right Triangle

Sketch the 2 dimensional polygon that was rotated:

*Solid Diagram:

*Views:

Base View: Lateral View:

*Cross Sections:

Parallel To Base: Perpendicular to Base:

What we need to know about cones...

A cone is... - a 3D solid figure with __________________________________________

Other Important Properties -________________ is the length from the center of base to the top

-_______________________________ is the length from the edge of the base to the top

Google Sketch Up!

Thinking in 3-D... Semi Circle

Sketch the 2 dimensional polygon that was rotated:

*Solid Diagram:

*Views:

Page 12: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

*Cross Sections:

What we need to know about spheres...

A sphere is... -3D closed surface

Other Important Properties

-set of points __________________________________ to one center point

-____________________________ is the distance from the center most point to the surface

Cross Sections in Spheres The Great Circle -The _________________________ possible cross section you can have in sphere

-always a __________________________

-same radius as the sphere

Page 13: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Applying our Knowledge 1) A right triangular flag is attached to a pole. The flag spins around the pole. a) What mathematical transformation best represents the situation? b) What is the resulting solid that would be formed? 2) A sphere is "sliced" open. Imagine looking at the half sphere. What would be the shape of the face of the half

sphere? 3) Take the shape you wrote for question 2. What figure would you get if you translated that shape into three

dimensions? 4) a) What figure would be created if the triangle were rotated around the y-axis? b) What is the radius of its base? c) What figure would be created if the triangle were rotated around the x-axis. d) What is the radius of its base?

Page 14: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

5) Find the length of the slant height of the following cone.

6) William is drawing pictures of cross sections of the right circular cone below.

Which drawing can not be a cross section of a cone?

1)

3)

2)

4)

7) Which figure can have the same cross section as a sphere?

1)

3)

2)

4)

8) If the rectangle below is continuously rotated about side w, which solid figure is formed? Sketch it!

Page 15: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

11-2 Homework

Directions: Answer the following questions to the best of your ability. Show all work.

1) Fill in the following charts for each solid provided:

Cross Section Perpendicular to base

Cross section parallel to base

2) What is the name of the following solid object? How could you form this solid using a transformation?

Name one other solid that has a cross section shape in common with this figure.

3) The radius of this sphere is 4 feet. Find the area of the great circle of this sphere to the nearest tenth.

4) The lateral faces of any prism are composed of 1) congruent isosceles triangles 3) congruent right triangles

2) rectangles 4) squares

Page 16: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

5) What figure would be created if the semi-circle below were rotated around the x-axis? Draw it!

6) Use the following diagram below to answer each part:

a) What 3D solid would result from rotating this rectangle about side Q?

b) The height of the solid use units: c) Radius of the base of the solid use units: d) What do you notice about the units? e) What should you be aware of moving forward in this unit?

7) A two-dimensional cross section is taken of a three-dimensional object. If this cross section is a triangle, what cannot be the three-dimensional object? (1) cone (2) pyramid (3) cylinder (4) rectangular prism

Page 17: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Volume of Prisms and Cylinders

Learning Goals: (1) What is volume and how do we find the volume of a prism and a cylinder?

(2) What is Calvalieri’s Principle?

Getting ready for today!

a) What is the name of the given solid?

b) What shape is the base of this solid?

c) What is the area of this base (B)?

Volume for Prisms or Cylinders

Where B is the AREA OF THE BASE (not the length of the base)

h is the height/depth of the prism/distance between the two bases

Looking back at the Do Now: - What is the volume formula that we just learned? Why do you think this formula makes

sense? (Think back to the idea of translating figures into 3 dimensions)

-Why was it significant to find the area of the base in the earlier problem? Example 1: Find the volume of the triangular prism.

11-3 Notes

Page 18: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Example 2: Based on the following diagram, what is the volume of this cylinder to the nearest 10th?

We should be thinking… What is the base?

What is the area of the base?

Which is the height? How do recognize it in the diagram?

Equal Volumes and Cavalieri’s Theorem

Consider the two figures below. Make a prediction! Do you think the two figures below can hold the same amount of fluid? Why or why not?

a)

What shape is the cross section parallel to the base?

Is the area of the cross section the same throughout

the solid?

What is the height?

b)

What shape is the cross section parallel to the base?

Is the area of the cross section the same throughout the

solid?

What is the height?

Let’s explore a bit further …….

Let’s go back to our first example! Looking at calculated volumes …

What do we notice here? Cylinder A) Cylinder B)

What factors contribute to this?

V = 𝜋r2h

= 𝜋(2)2(4)

=16𝜋 in3

V = 𝜋r2h

= 𝜋(2)2(4)

=16𝜋 in3

Page 19: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Cavalieri’s Principle: any two solids that …..

have the same area of the ____________ _____________ parallel to the base throughout the

height of the solid as well as the same ______________also have the same______________.

Example: Non-Example:

Let’s think! Morgan tells you that Cavalieri’s principle cannot apply to the prisms shown below because their bases

are different. Do you agree or disagree? Explain.

Now let’s see how we can apply this theorem!

The diagram below shows two figures. Figure A is a right triangular prism and figure B is an oblique triangular

prism. The base of figure A has a height of 5 and a length of 8 and the height of prism A is 14. The base of

figure B has a height of 8 and a length of 5 and the height of prism B is 14.

Use Cavalieri's Principle to explain why the volumes of these two triangular prisms are equal.

Page 20: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Time to Practice These Skills! Work with your partners and check in after #1!

1. Reese has a rectangular prism with a length of 10 centimeters, a width of 2 centimeters, and an unknown height. He

needs to build another rectangular prism with a length of 5 centimeters and the same height as the original prism.

The volume of the two prisms will be the same. Find the width, in centimeters, of the new prism.

Before you calculate, answer this!

If the volumes are equal and heights

are also equal, according to cavelieri’s

principle what else must be true?

Now let’s solve!

2)Find the volume of a rectangular prism with a length of 8 cm, a width of 10 cm, and a height of 4 cm. 3) Find the volume of a cube with an edge of 8 m.

Page 21: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

4) Find the volume of the following triangular prism.

5) The volume of a rectangular pool is 1,080 cubic meters. Its length, width, and depth are in the ratio . Find the

number of meters in each of the three dimensions of the pool.

6) A box in the shape of a cube has a volume of 64 cubic inches. What is the length of a side of the box?

1) in 3) 8 in

2) 16 in 4) 4 in.

7) Consider a stack of square papers that is in the form a right prism.

a) What is the volume of the prism?

b) When you twist the stack of papers, as shown at the right, do you change the volumes Explain your reasoning.

c) Use your conjecture to find the volume of the twisted stack.

Page 22: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

11-3 Homework

Directions: Answer all questions to the best of your ability.

1) If the area of the base of a triangular prism is 16 and the height is 20, find the volume.

2) Find the volume of the triangular prism.

3) Find the volume of a right circular cylinder with radius = 1.4m and height = 6m

a) in terms of

b) to the nearest cubic unit

4) A rectangular prism has an altitude of 12 inches and a base area of 32 inches. A second rectangular prism has a base

with length 7 in, an altitude of 12 in, and the same volume as the first prism. Find the width of the base to the

nearest tenth of an inch.

5) Each stack of memo papers contains 500 equally-sized sheets of paper. Compare their volumes. Explain your

reasoning.

Page 23: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

6) The prisms described below have the same height as the prism shown .Which of the two prisms has the same

volume as this prism? Explain your reasoning.

Prism A: The base is a right triangle with legs 8 inches and 5 inches.

Prism B: The base is a square with side lengths of 4.5 inches.

7) A fish tank in the shape of a rectangular prism has dimensions of 14 inches, 16 inches, and 10 inches. The tank

contains 1680 cubic inches of water. What percent of the fish tank is empty?

8) Perfume is in a bottle in the shape of a cylinder with a diameter of 3 inches and a height of 4 inches. The

manufacturer would like to package a new cylindrical bottle of perfume with a diameter of 2 inches. What would

the height of the new bottle be to the nearest tenth of an inch, if the perfume bottles will have the same volume?

Check the key

and see

how you did!!

Page 24: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Volume of Pyramids, Cones and Spheres

Today’s Learning Goal: How do we find the volume of pyramids, cones and Spheres, and how are they related to other

volume formulas we have learned?

Volume of a Pyramid

Let's explore... Reactivate: How do we find the volume of a prism? Let's see how this relates to the volume of a pyramid!

11-4 Notes

Do Now! Do this on your own!

Solid Formed by what transformation/s?

How many Bases?

What is the measure of the height?

Pyramid

Cone

Volume of a Pyramid:

Page 25: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Example 1: The diagram below is a regular pyramid. Find the volume of the pyramid to the nearest cubic unit.

What other solid could also be created by a dilation and translation?

Let’s try it!

Example 2: The diagram shows a cone of height 8 units and base radius 6 units. What is its volume in term of ?

The odd ball! :-)

Let's Try It!

What is the volume, to the nearest hundredth of a cubic inch, of a sphere with a radius of 5 inches?

Volume of a Cone:

Volume of a Sphere:

Page 26: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Group Work!

Directions: In your groups, you will advance through three sections. The Stretch will help you practice the basics of volume.

In the Jog section, you will pick it a notch. In the sprint you will go full speed into a real-life application. Support each

other at every point!

Stretch

1) Find the volume of a pyramid if the base is a right triangle with legs of 8 inches and 10 inches, and the height of the

pyramid is 27 inches. Round to the nearest tenths.

2) Find the volume of the right circular cone to the nearest cubic foot.

Jog

3. When Connie camps, she uses a tent that is in the form of a regular pyramid with a square base. The

length of an edge of the base is 9 feet and the height of the tent at its center is 8 feet. Find the volume of the

space enclosed by the tent to the nearest cubic foot.

Page 27: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

4. A pharmacist is filling medicine capsules. The capsules are cylinders with half spheres on each end. If the length of the cylinder is 12 mm and the radius is 2 mm, how many cubic mm of medication can one capsule hold? (Round answer to the nearest tenth of a cubic mm.)

Sprint

5. The water tower in the picture below is modeled by the two-dimensional figure beside it. The water tower

is composed of a hemisphere, a cylinder, and a cone. Let C be the center of the hemisphere and let D be the center of the

base of the cone.

If feet, feet, and , determine and state, to the nearest cubic foot, the volume of the water

tower.

Page 28: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

11-4 Homework

Directions: Answer the following questions to the best of your ability. Show all work to receive full credit.

1) Find the volume of a cone to the nearest tenth with a radius of 8inches and a height of 20 inches.

2) The American Heritage Center at the University of Wyoming is a conical building. If the height is 77 feet, and the area

of the base is about 38,000 square feet, find the volume of air that the heating and cooling systems would have to

accommodate. Round to the nearest tenth.

3) Find the volume of a pyramid that has a square base with an edge of 2 feet, and the height of the pyramid is 1.5 feet.

4) The volume of a pyramid is 576 cubic inches and the height of the pyramid is 18 inches. Find the area of the base.

6) If a golf ball has a diameter of 4.3 cm and a tennis ball has a diameter of 6.9cm, find the difference between the volumes of the 2 balls to the nearest tenth.

Page 29: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

7) A right cone has a height of 6 feet and a volume of 32 cubic feet. What is its radius to the nearest foot?

8) A child’s toy is fully filled with a heavy liquid in the hemisphere and lighter liquids in the cone and cylinder so that the

toy will always right itself (stand up straight) as it is shown in the picture. The slant height of the cone is 10 in, height of

cylinder is 16 in and the radius is 6. How much total liquid is contained inside of the toy to the nearest tenth?

Page 30: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Today’s Goal: How can we apply volume to real-life modeling problems?

Today we are going to be looking at real-life “models” that requires the knowledge of solids and its applications.

In your teams:

1. Read the problem, highlight/annotate any key words are pieces of information

2. Come up with a plan! Write any ideas, solve for anything you CAN solve for and reason through how you’ll get your answer!

Model 1) A shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 8.5 feet,

and a height of 4 feet. The container is completely filled with contents that weigh, on average, 0.25 pounds per cubic

foot. What is the weight, in pounds, of the contents in the container?

What’s our method?

Let’s Try it!

3. Think you have model #1? Check in with your teacher, then try model #2

Model 2) A hemispherical tank is filled with water and has a diameter of 10 feet. If water weighs 62.4 pounds per cubic

foot, what is the total weight of the water in a full tank, to the nearest pound?

SHOW WORK TO SUPPORT YOUR ANSWER CHOICE. Be prepared to explain yourself!

1) 16,336

2) 32,673

3) 130,690

4) 261,381

11-5 Notes

Page 31: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

DENSITY APPLICATIONS

There are 2 types of scenarios we encounter that deal with DENSITY In Geometry we look at both scenarios!

Today: Population Density -a ratio of the amount of a population that exists over a given area

Next Lesson: Density of a 3D Solid -a ratio that compares an object’s weight (mass) to the amount of space (volume) it takes up

Let’s take a look at population density first!

The diagram below shows two towns: Lollipop and West Lollipop. Each dot plotted in their area represents 20

individuals who live in that region. Which town do you think has a greater population density? Justify your answer.

Model 3) During an experiment, the same type of bacteria is grown in two petri dishes. Petri dish A has a diameter of 51

mm and has approximately 40,000 bacteria after 1 hour. Petri dish B has a diameter of 75 mm and has approximately

72,000 bacteria after 1 hour.

Determine and state which petri dish has the greater population density of bacteria at the end of the first hour.

Population density =

Page 32: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

11-5 Practice and Homework

1. Last Class, we saw the water tower problem. The water tower in the

picture below is modeled by the two-dimensional figure beside it.

The water tower is composed of a hemisphere, a cylinder, and a cone.

Here we were able to determine that the volume of the water tower is

7650 ft3.

Question: The water tower was constructed to hold a maximum of

400,000 pounds of water. If water weighs 62.4 pounds per cubic foot, can

the water tower be filled to 85% of its volume and not exceed the weight

limit? Justify your answer.

2. Molly wishes to make a lawn ornament in the form of a solid sphere. The clay being used to make the sphere

weighs .075 pound per cubic inch. If the sphere's radius is 4 inches, what is the weight of the sphere, to the nearest

pound?

1) 34

2) 20

3) 15

4) 4

Page 33: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

3. Walter wants to make 100 candles in the shape of a cone for his new candle business. The mold shown right will be

used to make the candles.

a) Each mold will have a height of 8 inches and a diameter of 3 inches. To the nearest cubic

inch, what will be the total volume of 100 candles?

b) Walter goes to a hobby store to buy the wax for his candles. The wax costs $0.10 per ounce. If the weight of

the wax is 0.52 ounce per cubic inch, how much will it cost Walter to buy the wax for 100 candles?

c) If Walter spent a total of $37.83 for the molds and charges $1.95 for each candle, what is Walter's profit

after selling 100 candles?

4. The population density of Huskyville is 17.5 Huskyvillers per acre. Exactly 840 Huskyvillers live in Huskyville.

How many acres does Huskyville cover?

Page 34: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

5. As of 2015 the most densely populated state in the US was New Jersey. The 2015 population of NJ was 8,957,907

people with 1218.1 people per square mile. Which choice is the approximate land area of the state of NJ to the

nearest square mile?

a. 7,135 square miles

b. 10,912 square miles

c. 7354 square miles

d. 12354 square miles

6. Log On to GOOGLE Classroom fill out today’s Form 11-5!

7. Complete today’s Looking Forward Question

8. Fill in the following:

a. Write all 2 solids formed by a translation and dilation:

b. What 3 solids have a cross section that is a circle?

c. What solid has a circular base and is formed by a translation?

d. What solid has a cross section parallel to the base of a triangle, and a cross section perpendicular to the base of a

rectangle?

e. What solid would have any cross section produce a circle?

Page 35: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Today’s Goal: How can we apply volume to real-life modeling problems?

Last Class: Population Density -a ratio of the amount of a population that exists over a given area

Today: Density of a 3D Solid -a ratio that compares an object’s weight (mass) to the amount of space (volume) it takes up

To calculate the Density of a solid we use the following formula

BE CAREFUL!

Tips for Density of Solid Problems:

*SOMETIMES YOU MUST CONVERT UNITS BEFORE STARTING THE PROBLEM

*If you can calculate volume in the problem, do that first!

Model 1) A wooden cube has an edge length of 6 centimeters and a mass of 137.8 grams. Determine the density of the

cube, to the nearest thousandth. State which type of wood the cube is made of, using the

density table below.

Before we proceed let’s Reactivate: Conversions:

Convert the following:

5.1 cm = ___________ meters

10.2 cm = ___________ meters

20.3 cm = ___________ meters

11-6 Notes

Page 36: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

Model 2) A contractor needs to purchase 500 bricks. The dimensions of each brick are 5.1 cm by 10.2 cm by 20.3 cm,

and the density of each brick is . The maximum capacity of the contractor’s trailer is 900 kg. Can the trailer

hold the weight of 500 bricks? Justify your answer.

a) Notice how density is given in kilograms per meters cubed? 1st convert dimensions of the brick so it’s in meters too!

b) Now volume of a brick.(Keep the long decimal)!

c) Fill into density formula; find the mass (weight) of one brick.

d) Can the trailer hold 500 bricks? Justify your answer!

Page 37: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

We are practicing! Complete the following problems, and the EdPuzzle! Check in Quiz Before Review in Class!

1. A cube has edges of 6cm and a density of 10 g/cm3.What is the mass of the cube?

2. Danielle has a full container of ice cream which has a density of 0.1 pounds per cubic inch. The container is a sphere

which has a radius of 3 inches. Marisa also has a full container of ice cream, which has a density of 0.01 pounds per

cubic inch and is contained in a sphere which has a radius of 3 inches.

How many more pounds of ice cream does Danielle have than Marisa (ie, the difference)? Round any decimals to the

nearest hundredth at the end of the problem.

3. A hot air balloon holds 74,000 cubic meters of helium, a very noble gas with the density of 0.1785 kilograms per

cubic meter. How many kilograms of helium does the balloon contain?

Page 38: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

4. The Property Brothers remodeled a kitchen and installed granite countertops.

A rectangular island in the kitchen now has a granite top measuring 5ft by 8

ft. by 1.2 inches. The density of granite is 2.7 g/in3.

How many grams is the weight of the island to the nearest tenth?

5. The HHS Math Talent show is giving out cylinder trophies this year to its winners. The trophy is a cylinder with a

height of 18 cm and a radius of 6 cm. The density of gold is 19.32 g/cm3 and the density of silver is

10.5 g/cm3.

How much heavier is the gold trophy compared to the silver to the nearest whole gram?

Page 39: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

6. Begin Flipped Video Lesson (prep for tomorrow)

Ready? Scenario:

It will take 2400 cubic inches of packing peanuts to fit in the following box.

It will take 1120 square inches of wrapping paper to cover the box (Without any overlap)

a) What information tells you about the volume of this box?

b) What information tells you about the surface area of this box?

c) What is surface area?

Surface Area

The surface area of a 3-Dimensional solid is... Here’s an example:

Find the surface area of a rectangular prism whose length is 6 meters, width is 4 meters, and height is 5.

Still unsure? Watch the video again! Complete next page; be prepared for a check in!

Page 40: Unit 11: Solid Geometry · Unit 11: Solid Geometry In this unit you must bring the following materials with you to class every day: Calculator Pencil This Booklet A device Headphones!

7. The rectangular prism shown below has a length of 3.0 cm, a width of 2.2 cm, and a height of 7.5 cm.

What is the surface area, in square centimeters?

8. Mr. Roberts is painting the outside of his son’s toy box, including the top and bottom. The toy box measures 3

feet long, 1.5 feet wide, and 2 feet high. What is the total surface area he will paint? (Hint: Draw the figure and

it’s net! OR remember our shortcut for rectangular prisms!)

You choose! Complete ONE of the following two problems, the right column is more of a challenge!

9. How many square inches of wrapping paper are needed

to entirely cover a box that is 2 ft by 3 ft by 6 ft?

9. Find the surface area of the figure below. Remember draw

and label the “net!!”