Volume of Hollow Cylinder

Introduction to volume of hollow cylinder:

          A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. The surface area and the volume of a cylinder have been known since deep antiquity.

The above figure represents the hollow cylinder. Formula for finding volume of hollow cylinder is

Formula:

`pi` R2h - `pi` r2h = `pi` h (R2 – r2)

Here R represents the radius of the outer surface

Similarly r represents the radius of the inner surface

Volume of Hollow Cylinder - Example Problems

Example: 1

Find the volume of the hollow cylinder with radius of the inner surface is 6 meter; radius of the outer surface is 8 meter and height is 9 meter.

Solution:

Already we know that volume of the hollow cylinder is `pi` h (R2 – r2)

Here R = 8 meter, r = 6 meter, h = 9 meter

Substitute this value into the formula we get

Volume = 3.14 * 9 (82 – 62)

Simplify the above equation we get

= 28.26 (64 – 36)

= 28.26 *28

= 791.28 meter cube

Therefore the volume of the hollow cylinder is 791.28 meter 3

Example: 2

Find the volume of the hollow cylinder with diameter of the inner surface is 22 meter; radius of the outer surface is 13 meter and height is 8 meter.

Solution:

We know the formula `pi` h (R2 – r2)

Here given is diameter of the inner surface we have to the radius

Radius = `(diameter ) / 2`

Radius = `22/2` = 11 meter

Now r = 11, R = 13, h=8 `pi` = 3.14

Substitute this value into the formula we get

Volume = 3.14 * 8 (132 – 112)

= 25.12 (169 – 121)

= 25.12 * 48

= 1205.76 meter cube

Therefore the volume of the hollow cylinder is 1205.76 meter3

I am planning to write more post on pre algebra practice test, what does prime factorization mean. Keep checking my blog.

Volume of Hollow Cylinder - Practice Problems:

Find the volume of the hollow cylinder with radius of the inner surface is 9 meter; radius of the outer surface is 12 meter and height is 11 meter.
Answer = 2177.12 meter 3

Find the volume of the hollow cylinder with diameter of the inner surface is 24 meter; diameter of the outer surface is 30 meter and height is 12 meter.
Answer = 3053.63 meter3