Watson- Math Studies Y1 Week of May 4th

Please complete the following assignments for the week. Label the problems clearly and

show all your work. The assignments you hand in will count for different

classwork/participation/homework grades out of 10 points each. You do not need to email the notes that you took on the video.

Monday • Video- Cylinder Surface Area and Volume

• Work due- Monday Worksheet

CW

Tuesday • Video: Sphere Surface area and Volume

• Work due- Tuesday Worksheet

CW

Wednesday • Classwork day (no video)

• Work due- 10H

HW

Thursday • Video: Study guide 10.3-10.5 odd #s

• Work due- Study guide 10.3-10.5 even #s

CW

Friday • No video

• Take home worksheet 10.3-10.5 due Monday

HW

• When assignment is completed, you can either

a. Use scanner to scan completed packet and email as an attachment to

nwatson@mvrcs.org , or

b. Take photos of each page of completed packet, email as attachments to nwatson@mvrcs.org

• You must submit the homework by the end of the day two days after it has been

assigned. For example, homework for the lesson on Monday can be submitted

without late penalty until end of Wednesday. Homework that is assigned on

Tuesday can be submitted without late penalty until end of Thursday and so on.

Collaboration is not allowed. Collaboration - to work jointly with others or together

especially in an intellectual endeavor. When collaboration takes place, all students must demonstrate understanding of the new material.

Monday Worksheet

IB Math Studies Cylinder Surface Area and Volume

Name:

1. A cylinder has a diameter of 5 cm and a height of 4 cm. Find its volume and surface area.

2. A cylinder has a surface area of 140𝜋 square centimeters, not including the top or bottom.

The height of the cylinder is 14 cm. Find the volume of the cylinder.

3. A column is made out of concrete, and is shaped like a cylinder that has a height of 3 m and a

diameter of 0.6 m. The density of the concrete is 2400 kg/m3.

a. Find the volume of the cylinder.

b. Hence find the weight of the column in kg.

4. A composite solid is made up of a cone on top of a cylinder. The height of the composite

solid is 25 cm. The radius of the cylinder is 6 cm, and the slant height of the cone is 10 cm.

Find the volume and surface area of the composite solid.

Tuesday Worksheet

IB Math Studies Sphere Surface Area and Volume

Name:

Example 1: The radius of a baseball is 3 in. Calculate its volume and surface area.

Example 2: The diameter of a soccer ball is 22 cm. Calculate its volume and surface area.

Example 3: A basketball measures 75 cm in circumference. Calculate its volume and surface

area to 3 sf.

Example 4: A gelcap is shaped like a cylinder that is capped with hemispheres on both ends.

The length of the cylinder is 5 mm and the radius of the cylinder is 1 mm. Find the volume and

surface area.

1. A yoga ball has a volume of 1 m3. Find the radius of the ball, then find the surface area.

2. An ice cream cone is 6 inches in height and 2.5 inches in diameter. A hemispherical scoop of

ice cream sits perfectly atop the cone. Find the volume of the two together.

3. A cannonball is shaped like a sphere. Its diameter is 5.55 inches and it weighs 24 lb. Find

the density of the metal that makes up the cannonball.

4. A solid hemisphere of foam has a total surface area of 900 cm2.

a. Find the radius of the foam.

b. If the foam has a density of 0.0192 g cm-3, find the weight of the hemisphere.

IB Math Studies Y2 Name:

STUDY GUIDE [10.3 – 10.5]

Example Problems – Solve on separate paper and turn in on test day!

1 Find the volume and surface area of the prism shown in Figure 1.

Figure 1

Figure 2

2 A cylindrical pencil is 13.5 cm long with a diameter of 0.7 cm. It is sharpened to a cone as

shown in Figure 2. After sharpening, the length of the cylindrical part is now 12.3 cm.

a i Write down the value of ℎ.

ii Find the value of ℓ.

b i Find the total surface area of the pencil.

ii Find the volume of the pencil.

c The pencil weighs 4 g. Find the density of the pencil, in g cm-3.

3 An artist decided to make 75 spherical cannonballs out of brass as part of a new piece. Each

ball is spherical and has a diameter of 10 cm.

a Calculate the total volume and surface area of the cannonballs (total).

The artist, being fickle, changed his mind the next day and melted down the cannonballs. He

then reforged the metal into the shape of a cone whose radius was 20 cm.

b Calculate the height of the cone.

c Calculate the surface area of the cone (including the bottom).

The artist changed his mind again and reforged the cone into the shape of a square pyramid

with a height of 15 cm.

d Find the side length of the base.

42°

8 cm

5.7 cm

Diagram not to scale

4 Jenny has a circular cylinder with a lid. The cylinder has a height of 39 cm and a diameter of

65 mm.

a Calculate the volume of the cylinder in cm3.

b There is a label covering the side of the cylinder. Calculate the area of that label.

The cylinder is used to store tennis balls. Each ball has a radius of 3.2 cm.

c Calculate how many tennis balls Jenny could vertically stack in the cylinder.

d Jenny fills the cylinder with as many tennis balls as possible and puts the lid on.

Calculate the volume of air inside the cylinder.

e Convert your answer from (d) into cubic meters.

5 Figure 3 shows a cuboid that has a base that measures 22.5 cm by 30 cm. The height is

unknown. The angle that 𝐴𝐺 makes with 𝐴𝐵𝐶𝐷 is 75o.

a Calculate the length of 𝐴𝐶.

b Find 𝐶𝐺 correct to the nearest cm.

c Hence find the surface area of the cuboid.

Figure 3

Figure 4

6 Figure 4 shows a rectangular prism with some side lengths and diagonal lengths marked.

𝐴𝐶 = 10 cm, 𝐶𝐻 = 10 cm, 𝐸𝐻 = 8 cm, and 𝐴𝐸 = 8 cm.

a Calculate the length of 𝐴𝐻.

b Find the size of angle 𝐴𝐶𝐻.

c Find the length of 𝐶𝐷.

d The prism is made of styrofoam, which has a density of 0.032 g per cm3. Find the

weight of the prism.

Name:________________________________

Math Studies Take Home Worksheet 10.3-10.5

1 A child’s toy is made by combining a hemisphere of radius 6 cm and a right circular

cone of slant height ℓ as shown on the diagram below.

a Show that the volume of the hemisphere is 144𝜋 cm3. [2]

The volume of the cone is three-fourths that of the hemisphere.

b Show that the vertical height of the cone is 9 cm. [4]

c Calculate the slant height ℓ of the cone. [2]

d Calculate the angle between the slanted side and the base of the cone. [3]

e Calculate the total surface area of the toy, correct to the nearest 1 cm2. [5]

f The toy is made of balsa wood, which has a density of 0.16 g per cm3. Calculate the total weight of the toy. Give your answer correct to the nearest tenth. [3]

[Note: there is additional space for this problem on the next page!]

2 Tennis balls are sold in cylindrical tubes that contain three tennis balls each, stacked vertically. The radius of each tennis ball is 3.35 cm and the radius of the tube is 3.40 cm. The length of the tube is 21 cm.

a Find the volume of one tennis ball. [2]

b Calculate the volume of the empty space in the tube when three tennis balls have been placed in it. [5]

3 The following diagram shows a cabin (shaped like a rectangular prism) with a sloping

roof (shaped like a triangular prism). The sloping edges of the roof (𝐴𝐷𝐹𝐶 and 𝐴𝐷𝐸𝐵)

are rectangles. Angle 𝐴𝐶𝐷 is 46°, the vertical height 𝐴𝑀 of the roof is 4 m, the length

of the roof 𝐶𝐹 is 11 m, and the height of 𝐶𝑍 is 6 m.

a Calculate 𝐴𝐶. [2]

b Find the length of 𝐵𝐶. [2]

c Hence show that the surface area of the cabin is 378 m2, correct to the nearest m2. (Note that the surface area includes the walls, the roof, but not the floor.) [5]

4 Bob invests 2000 USD in a bank that offers simple interest at a rate of 2.5% per annum.

a Bob’s money will double in 𝑛 years. Calculate the value of 𝑛. [3]

Charles invests 2000 USD in a bank that offers compound interest at a rate of 2% per annum, compounded quarterly.

b Find the amount of money that Charles will have after 𝑛 years, where 𝑛 is the

number of years that it took Bob’s money to double.) [2]