Practice Volume of a Cylinder in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The amount of three-dimensional space inside a cylinder, found by multiplying the area of the circular base by the height.

Imagine stacking hundreds of identical circular coins into a tall tower. Each coin is a thin circle with area πr2\pi r^2, and stacking hh units high gives you a cylinder. The volume is just the area of one coin times the height of the stack.

Showing a random 20 of 50 problems.

Example 1

hard
A hollow cylindrical pipe has outer radius 55, inner radius 44, and length 2020. Find the volume of material.

Example 2

medium
How many liters does a cylindrical drum of radius 0.3 m and height 1 m hold? (1 m³ = 1000 L, π≈3.14\pi \approx 3.14.)

Example 3

easy
If you double a cylinder's height, what happens to its volume?

Example 4

challenge
Using Cavalieri's principle, explain why an oblique (slanted) cylinder has the same volume as a right cylinder with the same base and height.

Example 5

medium
A pipe is a hollow cylinder: outer radius 5, inner radius 3, length 10. Find the volume of material in terms of π\pi.

Example 6

easy
If you double a cylinder's radius (height fixed), what happens to its volume?

Example 7

easy
A cylinder's base area is 36π36\pi and its height is 55. Find its volume.

Example 8

medium
A water bottle is a cylinder with radius 33 cm and height 2020 cm. How many milliliters does it hold? (1 cm3=1 mL1\text{ cm}^3=1\text{ mL}, use π≈3.14\pi\approx 3.14.)

Example 9

easy
A cylinder has a radius of 4 cm and a height of 10 cm. Find its volume. Use π≈3.14\pi \approx 3.14.

Example 10

medium
A pool is a cylinder with radius 55 m and depth 22 m. How many cubic meters of water does it hold? Leave answer in terms of π\pi.

Example 11

medium
A cylinder's radius is tripled while its height stays the same. By what factor does its volume change?

Example 12

hard
A cylindrical silo has volume 1000π1000\pi m³ and height 1010 m. Find its diameter.

Example 13

hard
A cylindrical tank of radius 22 m is being filled at 4π4\pi m³/min. How fast (in m/min) does the water level rise?

Example 14

easy
A cylinder has radius 3 and height 10. Find its volume in terms of π\pi.

Example 15

medium
A cylinder's height equals its diameter. If the radius is rr, write its volume in terms of rr and π\pi.

Example 16

medium
A cylinder has volume 108π108\pi and height 33. Find its radius.

Example 17

easy
What is the volume of a cylinder with radius 66 and height 00?

Example 18

medium
Water in a cylinder of radius 33 has depth 88. The water is poured into an empty cylinder of radius 44. Find the new depth.

Example 19

challenge
A cylindrical glass of radius 4 is tilted until water just reaches the rim on one side and the base edge on the other. If full height is 10, estimate the water volume as half-full reasoning suggests.

Example 20

easy
What does rr stand for in the cylinder volume formula V=πr2hV=\pi r^2 h?
← Back to Volume of a Cylinder Worked Examples Formula Explained