Assignment · Assignment Assignment for Lesson 12.1 Name _ Date _ Box It Up Nets and...

Chapter 12 l Assignments 227

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Assignment Assignment for Lesson 12.1

Name _____________________________________________ Date ____________________

Box It Up Nets and Platonic Solids

Determine whether each solid is a polyhedron. Explain your reasoning.

1. 2.

3. 4.

5. Use the polyhedron shown to complete parts (a) through (e).

228 Chapter 12 l Assignments

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a. Determine the number of vertices of the polyhedron.

b. Determine the number of faces of the polyhedron.

c. Determine the number of edges of the polyhedron.

d. Describe the polygons used to create the polyhedron.

e. Is the polyhedron a regular polyhedron? Explain why or why not.

6. Create a net for a tetrahedron on the grid shown.


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7. Describe the polyhedron that is represented by the net shown with respect to

vertices, faces, edges, and overall shape.

8. Describe the polyhedron that is represented by the net shown with respect to

vertices, faces, edges, and overall shape.


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Name _____________________________________________ Date ____________________

Backyard Barbecue Introduction to Volume and Surface Area

1. You want to build a rectangular storage box to hold barbecue supplies for your

new patio.

a. How many measurements are involved in building the storage box?

Describe these measurements.

b. You want the box to have a rectangular base with a length of 5 feet and a width

of 3.5 feet. You want the box to be 2 feet tall. Sketch a model of the storage

box and label the measurements.

c. You are going to cover the outside of the storage box with a special rainproof

coating. What is the area that you will be covering?


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d. You are going to cover the top and sides of the storage box with 12-inch by

12-inch tiles. The tiles are sold in boxes of 20. How many boxes of tiles will you

need to purchase? Explain your reasoning.

e. How much space is inside of the storage box?


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Calculate the surface area of each figure.

2.

5 m

12 m

13 m

15 m

3.

4 in.

4 in.

2 in.

2 in.

2 in.

2 in

6 in.

Calculate the volume of each figure.

4.

1.25 yd2.5 yd

6.75 yd

5.

16 ft

10 ft

22 ft

10 ft

6 ft


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Name _____________________________________________ Date ____________________

Turn Up the Volume and Let’s Bend Light Beams Volume and Surface Area of a Prism

Name each prism.

1. 2.

Create a sketch of each prism.

3. Pentagonal prism 4. Right triangular prism


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5. You want to build a storage shed in your back yard for your lawn equipment.

Two designs for the shed are shown below.

8 feet

12 feet

6 feet

Shed A

8 feet

8 feet

6 feet

4 feet

Shed B

a. What is the volume of Shed A?

b. What is the volume of Shed B?

c. Suppose that you want to build a shed that gives you the most space inside.

Which shed should you choose?


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6. You are designing a box in the shape of a rectangular prism for a shipping

company. The box must have a volume of 24 cubic feet.

a. Complete the table with possible whole number dimensions for the box and

calculate the corresponding surface areas.

Length (ft) Width (ft) Height (ft) Volume (ft3) Surface Area (ft2)

24

24

24

24

24

24

b. What are the dimensions of the box with the greatest surface area?

c. What are the dimensions of the box with the smallest surface area?

d. Which box do you think the shipping company would prefer?

Explain your reasoning.


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Name _____________________________________________ Date ____________________

Modern-Day Pyramids and Soundproofing Volume and Surface Area of a Pyramid

Name each pyramid.

1. 2.

Create a sketch of each pyramid.

3. Right triangular pyramid 4. Hexagonal pyramid

5. The Luxor Hotel in Las Vegas is a replica of Khafre Pyramid at Giza, one of the

seven wonders of the world. The Luxor’s base is a square with a side length of

646 feet, and it is 350 feet tall.

a. What is the volume of the Luxor Hotel?


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b. The Khafre Pyramid has a volume of 2,226,450 cubic meters. Its base is a

square with a side length of 215 meters. What is the height of the

Khafre Pyramid?

6. A store sells square pyramid-shaped scented candles. The dimensions of two of

the candles are shown below.

6 cm6 cm

16 cm

Candle A

8 cm 8 cm

9 cm

Candle B

a. Calculate the slant height of each candle.

b. Calculate the surface area of each candle.


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c. Calculate the volume of each candle.

d. Both candles are made of wax. Which candle contains more wax? Explain.

e. Both candles are sold in a plastic wrapping. Which candle requires more plastic

wrapping? Explain.


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Name _____________________________________________ Date ____________________

Making Concrete Stronger Volume and Surface Area of a Cylinder

Calculate the surface area of each cylinder. Use 3.14 for � and round to the nearest tenth, if necessary.

1.

9 mm

25 mm

2. 15 ft

14 ft

Calculate the volume of each cylinder. Use 3.14 for � and round to the nearest tenth, if necessary.

3. 26 in.

151 in.

4.

200 cm

275 cm


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5. A tunnel through a mountain is in the shape of half of a cylinder. The entrance to

the tunnel is 40 feet wide, as shown. The tunnel is 800 feet long.

40 ft

a. How much of the mountain had to be displaced to build the tunnel?

b. The inside of the tunnel is lined with cement, which includes the arc of the

tunnel and the road. How much cement was used?


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6. Your municipality is replacing the storage tanks in the community. In which plan is

the total capacity greater?

Plan 1: Install one cylindrical tank that is 150 feet tall and has a radius of 50 feet.

Plan 2: Install two cylindrical tanks that are 75 feet tall. One cylindrical tank has a

radius of 30 feet and one tank has a radius of 25 feet.

Use 3.14 for � and round your answers to the nearest tenth if necessary.


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Name _____________________________________________ Date ____________________

Sand Piles Volume and Surface Area of a Cone

Calculate the volume of each cone described. Use 3.14 for � and round to the nearest tenth, if necessary.

1. A traffic cone has a radius of 9 inches and a height of 30 inches.

2. A funnel that is used to change the oil in a car is in the shape of a cone.

The base of the funnel has a circumference of 60 centimeters. The height of the

funnel is 25 centimeters.

3. A mini ice cream cone has a diameter of 3.5 centimeters and a height

of 6 centimeters.


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4. A cone has a radius of 6 meters and a height of 8 meters. Use this information

to complete parts (a) through (c). Use 3.14 for � and round to the nearest tenth,

if necessary.

a. Draw a sketch of the cone and label its measurements.

b. Calculate the slant height of the cone.

c. Calculate the surface area of the cone.


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Use the given information to calculate the missing measures for each cone. Write your answers in terms of �. Show all your work.

5. Height � 6. Height � 39 yd

Radius � 5 ft Radius �

Slant height � Slant height � 65 yd

Surface area � Surface area �

Volume � 100� ft3 Volume �


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Name _____________________________________________ Date ____________________

Walk in the Footsteps of Archimedes Volume and Surface Area of a Sphere

Calculate the surface area of each sphere. Use 3.14 for � and round to the nearest tenth, if necessary.

1.

14 in.

2.

2.5 cm

Calculate the volume of each sphere. Use 3.14 for � and round to the nearest tenth, if necessary.

3.

21 mm

4.

45 ft


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5. A can holds 3 tennis balls as shown in the figure. The radius of each

3 cm

3 cm

3 cm

tennis ball is 3 centimeters.

a. What is the volume of a single tennis ball?

b. What is the total volume all 3 tennis balls take up?

c. Can you determine the height of the can? Explain your reasoning.

d. What is the volume of the can? Use 3.14 for �.

e. What is the volume of the can not taken up by the tennis balls?

6. A new umbrella design was created in the shape of a hemisphere with a special

plastic coating on the material to better repel water. The diameter of the

umbrella is about 1 yard. Because the umbrella is still in its beginning stages,

the manufacturer only produces 200 of them to be sold in select markets.

How much of the specially coated material must be produced for the manufacture

of these umbrellas?

Assignment · Assignment Assignment for Lesson 12.1 Name _ Date _ Box It Up Nets and...

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Transcript of Assignment · Assignment Assignment for Lesson 12.1 Name _ Date _ Box It Up Nets and...

Assignment · Assignment Assignment for Lesson 12.1 Name _____ Date _____ Box It Up Nets and...

Documents

Transcript of Assignment · Assignment Assignment for Lesson 12.1 Name _____ Date _____ Box It Up Nets and...

Assignment · Assignment Assignment for Lesson 12.1 Name _ Date _ Box It Up Nets and...

Transcript of Assignment · Assignment Assignment for Lesson 12.1 Name _ Date _ Box It Up Nets and...