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# Volume of Cylinders – Explanation & Examples

**The volume of a cylinder is the measure of the amount of space occupied by a cylinder or the measure of the capacity of a cylinder.**

This article will show you how to find the volume of a cylinder by using cylinder volume formula.

**In geometry, a cylinder is a 3-dimensional shape with two equal, and parallel circles joined by a curved surface.**

The distance between the circular faces of a cylinder is known as the **height of a cylinder**. The top and bottom of a cylinder are two congruent circles whose radius or diameter are denoted as ‘**r**’ and ‘**d**’, respectively.

## How to Find the Volume of a Cylinder?

To **calculate the volume of a cylinder,** you need the radius or diameter of the circular base or top and a cylinder’s height.

The **volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder. The volume of a cylinder is measured in cubic units.**

*Calculation of the volume of a cylinder is useful when designing cylindrical objects such as:*

- Cylindrical water tanks or wells
- Culverts
- Perfume or chemical bottles
- Cylindrical containers and pipes
- Cylindrical flasks used in chemistry labs

### Cylinder volume formula

The formula for the volume of a cylinder is given as:

**Volume of a cylinder = πr ^{2}h **cubic units

Where πr^{2} = area of a circle;

π = 3.14;

r = radius of the circular base and;

h = height of a cylinder.

For a hollow cylinder, the volume formula is given as:

**Volume of a cylinder = πh (r _{1}^{2} – r_{2}^{2})**

Where, r_{1} = external radius and r_{2 }= internal radius of a cylinder.

The difference of the external and internal radius forms the wall thickness of a cylinder i.e.

Wall thickness of a cylinder = r_{1} – r_{2 }

Let’s solve a few example problems about the volume of cylinders.

*Example 1*

The diameter and height of a cylinder are 28 cm and 10 cm, respectively. What is the volume of the cylinder?

__Solution__

Given;

The radius is half of the diameter.

Diameter = 28 cm ⇒ radius = 28/2

= 14 cm

Height = 10 cm

By the cylinder volume formula;

volume = πr^{2}h

= 3.14 x 14 x 14 x 10

= 6154.4 cm^{3}

So, the volume of the cylinder is 6154.4 cm^{3}

*Example 2*

The depth of water in a cylindrical tank is 8 feet. Suppose the radius and height of the tank are 5 feet and 11.5 feet, respectively. Find the volume of water required to fill the tank to the brim.

__Solution__

First calculate the volume of the cylindrical tank

Volume = 3.14 x 5 x 5 x 11.5

= 902.75 cubic feet

Volume of water in the tank = 3.14 x 5 x 5 x 8

= 628 cubic feet.

The volume of water required to fill the tank = 902.75 – 628 cubic feet

= 274.75 cubic feet.

*Example 3*

The volume of a cylinder is 440 m^{3}, and the radius of the base is 2 m. Calculate the height of the tank.

__Solution__

Volume of a cylinder = πr^{2}h

440 m^{3} = 3.14 x 2 x 2 x h

440 = 12.56h

By dividing 12.56 on both sides, we get

h = 35

Therefore, the height of the tank is 35 meters.

*Example 4*

The radius and height of a cylindrical water tank are 10 cm and 14 cm, respectively. Find the volume of the tank in liters.

__Solution__

Volume of a cylinder = πr^{2}h

= 3.14 x 10 x 10 x 14

= 4396 cm^{3}

Given, 1 Liter = 1000 cubic centimeter (cm^{3})

Therefore, divide 4396 by 1000 to get

Volume = 4.396 liters

*Example 5*

The external radius of a plastic pipe is 240 mm, and the internal radius is 200 mm. If the pipe’s length is 100 mm, find the volume of material used to make the pipe.

__Solution__

A pipe is an example of a hollow cylinder, so we have

Volume of a cylinder = πh (r_{1}^{2} – r_{2}^{2})

= 3.14 x 100 x (240^{2} – 200^{2})

= 3.14 x 100 x 17600

= 5.5264 x 10^{6 }mm^{3}.

*Example 6*

A cylindrical solid block of a metal is to be melted to form cubes of edge 20 mm. Suppose the radius and length of the cylindrical block are 100 mm and 490 mm, respectively. Find the number of cubes to be formed.

__Solution__

Calculate the volume of the cylindrical block

volume = 3.14 x 100 x 100 x 490

= 1.5386 x 10^{7} mm^{3}

Volume of the cube = 20 x 20 x 20

= 8000 mm^{3}

The number of cubes = volume of the cylindrical block/volume of the cube

= 1.5386 x 10^{7} mm^{3}/ 8000 mm^{3}

= 1923 cubes.

*Example 7*

Find the radius of a cylinder with the same height and volume as a cube of sides 4 ft.

__Solution__

Given:

Height of cube = height of cylinder = 4 feet and,

volume of the cube = volume of cylinder

4 x 4 x 4 = 64 cubic feet

But volume of a cylinder = πr^{2}h

3.14 x r^{2 }x 4 = 64 cubic feet

12.56r^{2} =64

Divide both sides by 12.56

r^{2 }= 5.1 feet.

r = 1.72

Therefore, the radius of the cylinder will be 1.72 feet.

*Example 8*

A solid hexagonal prism has a base length of 5 cm and a height of 12 cm. Find the height of a cylinder with the same volume as the prism. Take the radius of the cylinder to be 5 cm.

__Solution__

The formula for the volume of a prism is given as;

Volume of a prism = (h)(n) (s^{2})/ [4 tan (180/n)]

where, n = number of sides

s = base length of a prism

h = height of a prism

Volume = (12) (6) (5^{2})/ (4tan 180/6)

=1800/2.3094

=779.42 cm^{3}

Volume of a cylinder = πr^{2}h

779.42 =3.14 x 5 x 5 x h

h = 9.93 cm.

So, the height of the cylinder will be 9.93 cm.

*Practice Questions*

- If the cylindrical paint box’s volume and radius are 640π cubic cm and 8 cm, respectively, what is its height?
- Consider a cylindrical tank whose height is two times its radius. If the volume of the tank is 4580 units, what is the radius of the tank?

__Answers__

- 10 cm
- 9 units