 # Volume of Cylinders

Solid geometry is concerned with three-dimensional shapes.

In these lessons, we will learn:
• how to find the volume of cylinders
• how to find the volume of hollow cylinders or tubes or pipes
• how to solve word problems about cylinders.

Related Topics:
More Geometry Lessons

How to find the Volume of Solid Cylinders?

A cylinder is a solid with two congruent circles joined by a curved surface. In the above figure, the radius of the circular base is r and the height is h.

The volume of the cylinder is the area of the base × height. Since the base is a circle and the area of a circle is πr2 then the volume of the cylinder is πr2 × h.

Volume of cylinder = πr2h

Surface Area of cylinder = 2πr2 + 2πrh

Worksheet - Calculate volume of cylinders
Worksheet - Calculate surface area of cylinders
Worksheet - Calculate volume & surface area of cylinders
Worksheet - Calculate surface area of cylinders & pipes

Example:

Calculate the volume of a cylinder where:

a) the area of the base is 30 cm 2 and the height is 6 cm.
b) the radius of the base is 14 cm and the height is 10 cm.

Solution:

a) V = Area of base × height
= 30 cm2 × 6 am
= 180 cm3

b) How to find the volume of a cylinder?
Examples:
1. Find the volume of cylinder with radius of 5.5 feet and a height of 11.4 feet.
2. Find the volume of cylinder with diameter of 12 inches and a height of 29 inches. How to find the volume of a right cylinder?
Example:
Find the volume with r = 9 in and h = 12 in. (Leave your answer in &oi; form) How to find the volume of Hollow Cylinders?

Sometimes you may be required to calculate the volume of a hollow cylinder or tube or pipe. Volume of hollow cylinder:
= πR2 h – πr2 h
= πh (R2– r2)

Example:

The figure shows a section of a metal pipe. Given the internal radius of the pipe is 2 cm, the external radius is 2.4 cm and the length of the pipe is 10 cm. Find the volume of the metal used. Solution:

The cross section of the pipe is a ring:
Area of ring = [ π (2.4)2– π (2)2]= 1.76 π cm2

Volume of pipe = 1.76 π × 10 = 55.3 cm3
Volume of metal used = 55.3 cm3

How to find the volume of a cylinder in a prism?
Examples:
A cylindrical can is packed securely in a box.
a) Find the radius and height of the can.
b) What is the volume of the empty space between the can and the box?
c) Find the ratio of the volume of the can to the volume of the box.

How to solve word problems about cylinders?

These videos show how to solve word problems about cylinders.

Examples:
1. A cylindrical can is packed in a box. What is the volume of empty space between the can and the box?

2. Emma has two prism-shaped containers. One has a volume of 9 1/3 cubic feet. How many smaller prisms would it take to fill the larger prism?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  