A cylinder is similar to a rectangular solid except that the base is a circle instead of a rectangle. The volume of a cylinder is the area of its circular base times its height. The amount of space occupied by the cylinder is called its volume. It unit of measurement is cubic units.
The volume of a cylinder whose base has radius 'r' and whose height is 'h' is V = $\pi r^2$ h.

Volume of a cylinder is the product of area of the cylinder and its height. The formula for volume is depends on the area of the cylinder and its height. The volume of a cylinder is represented by cubic units.

Cylinder

The area of a cylinder can be written as, A = $\pi$ * r2.

=> Volume of cylinder = $\pi$ r2 h

Here, $\pi$ is the constant variable, r is the radius of the cylinder and h is the height of the cylinder.
The constant variable $\pi$ is equal to $\frac{22}{ 7}$ or 3.14
Volume of a cylinder is the number of units used to fill a cylinder. Volume of a cylinder is a measurement of the occupied units of a cylinder. The volume is represented by cubic units like cubic centimeter, cubic millimeter and so on. Volume of a cylinder is the product of area of base of the cylinder and its height.

Formula:

The Volume of the Cylinder can be written as,

V = $\pi r^2$h


where,
V = Volume of a cylinder
r = Radius of a cylinder
h = Height of a cylinder.

To find the volume of the cylinder, we have to multiply the height of the cylinder to its area. Firstly find the area of the cylinder (using formula A = $\pi$ * r2) and then multiply with the height of the cylinder. The volume of a cylinder is represented by cubic units.

Steps for Finding the Volume of the Cylinder:

Step 1: Find the area of the cylinder.

Step 2: Multiply the area of the cylinder and height of the cylinder.

Step 3
: Write answer in the proper square unit of measurement.

Example 1:


Find the volume of the cylinder having radius 4 cm and height 6 cm.

Solution:

Cylinder

Step 1:

Radius of the cylinder (r) = 4 cm
Height of the cylinder (h) = 6 cm

Step 2:

Volume of a cylinder (V) = $\pi$ r2 h

= $\frac{22}{7}$ * 42 * 6

= $\frac{22}{7}$ * 4 * 4 * 6

= 301.71

Hence the volume of a cylinder is 301.71 cm3 .

Example 2:
If the height of a cylinder is increased by 20% but radius of its base remains the same, then its volume will be increased by how many percent.

Solution:

Let the initial height and radius of the cylinder be 'h' and 'r' respectively

Step 1:

Initial volume of the cylinder = $\pi r^2$ h

and increased height = $\frac{100 + 20}{100}$ h

= $\frac{12}{10}$ h

Step 2:

Volume of the resulting cylinder = $\frac{\pi r^2 * 12 h}{10}$

Increased volume of the cylinder = $\frac{12\pi r^2 h}{10}$ - $\pi r^2$ h

= $\frac{2\pi r^2 h}{10}$

Therefore % increase in volume = $\frac{2\pi r^2 h}{10}$ x $\frac{100}{\pi r^2 h}$

= 20 %

Hence the volume of the cylinder will be increased by 20%.