Volume of Cylinders, Cones and Spheres: math practice, Grade 8 – download the PDF

1 A cylinder ★★★

A cylinder has a radius of 5 cm and a height of 10 cm.

a. Find its exact volume in terms of \(\pi\). b. Give an approximation using \(\pi \approx 3.14\).

2 A cone ★★★

A cone has a base radius of 3 inches and a height of 7 inches. Find its volume in terms of \(\pi\).

3 A sphere ★★★

A sphere has a radius of 3 feet. Find its volume in terms of \(\pi\).

4 True or false? ★★★

Decide whether each statement is true or false, and justify.

1. A cone and a cylinder have the same base and the same height. The cone has half the volume of the cylinder.
2. The volume of a sphere is measured in square units.

5 Diameter given ★★★

A cylindrical drum has a diameter of 8 m and a height of 5 m. Find its volume using \(\pi \approx 3.14\).

6 Cone from cylinder ★★★

A cylinder has a volume of \(90 \text{ cm}^3\). A cone has the same base and the same height. What is the volume of the cone?

7 A glass ball ★★★

A solid glass ball has a radius of 6 cm. Find its volume to the nearest tenth, using \(\pi \approx 3.14\).

8 A can of soup ★★★

A can of soup has a diameter of 7 cm and a height of 10 cm. Use \(\pi \approx 3.14\).

1. Find the volume of the can.
2. The label says the can holds 400 mL of soup. Is that possible? Remember \(1 \text{ mL} = 1 \text{ cm}^3\).

9 A water tank ★★★

A cylindrical tank has a radius of 2 ft and a height of 6 ft. Use \(\pi \approx 3.14\) and \(1 \text{ ft}^3 \approx 7.48\) gallons. How many gallons does it hold, to the nearest gallon?

10 A sand pile ★★★

Sand forms a cone-shaped pile with a base diameter of 6 m and a height of 2 m. A truck carries 4 \(\text{m}^3\) per trip. Use \(\pi \approx 3.14\). How many trips are needed to carry all the sand?

11 Find the height ★★★

A cone has a volume of \(48\pi \text{ cm}^3\) and a base radius of 4 cm. Find its height.

12 Find the radius ★★★

A cylinder has a volume of \(200\pi \text{ cm}^3\) and a height of 8 cm. Find its radius.

13 A glass globe ★★★

A decorative glass globe has a diameter of 10 cm. Find its volume to the nearest tenth, using \(\pi \approx 3.14\).

14 A bowl ★★★

A bowl is shaped like a hemisphere with a radius of 6 inches. Use \(\pi \approx 3.14\). How much water does it hold when it is full?

15 An ice cream cone ★★★

An ice cream cone has a base radius of 3 cm and a height of 10 cm. It is topped with a scoop shaped like a hemisphere of radius 3 cm.

Find the total volume, first in terms of \(\pi\), then to the nearest hundredth using \(\pi \approx 3.14\).

16 A metal pipe ★★★

A solid metal pipe is 20 cm long. Its outer radius is 5 cm and a cylindrical hole of radius 3 cm goes all the way through it. Use \(\pi \approx 3.14\). How much metal does the pipe contain?

17 A ball in a tube ★★★

A ball fits exactly inside a cylindrical tube: its radius is 3 cm and the tube is 6 cm tall.

a. Find the volume of the tube and the volume of the ball in terms of \(\pi\). b. What fraction of the tube does the ball fill? c. Find the volume of empty space, using \(\pi \approx 3.14\).

18 Changing dimensions ★★★

A cylinder has a radius of 3 cm and a height of 5 cm. Find how its volume changes when: a. the radius is doubled; b. the height is doubled; c. both are doubled.

19 Pouring a cone ★★★

A paper cup shaped like a cone has a radius of 4 cm and a height of 12 cm. It is full of water, and the water is poured into an empty cylindrical glass with a radius of 4 cm. How high does the water rise in the glass?

20 Radius of a sphere ★★★

A spherical storage tank has a volume of \(972\pi \text{ m}^3\). Find its radius.

21 A marble in a fish tank ★★★

A cylindrical tank has a radius of 15 cm and contains water. A solid ball of radius 3 cm is dropped in and sinks completely. By how many centimeters does the water level rise?

22 A grain silo ★★★

A grain silo is a cylinder with a cone-shaped roof.

Find the volume of the whole silo, in terms of \(\pi\), then using \(\pi \approx 3.14\).