Volume of Cylinder Formula

# Volume of Cylinder Formula

## Volume of Cylinder

We have observed that a cuboid is made up with the rectangles. A right circular cylinder is also made up with circles (circular discs) of the same size stacked together one above the other.

We know that the volume of a cuboid = l × b × h = (l × b) × h = Area of base × height

We can extend this to find the volume of a cylinder, since area of base = area of circle.

Therefore, volume of a cylinder = area of base × height

= πr2 × h = πr2h cubic units

Thus, Volume of a cylinder = πr2h

where r is the radius of the base and h is the height of the right circular cylinder.

Also, the value of π is 22/7 or 3.14.

### Volume of Cylinder Formula

Volume of a cylinder = πr2h

Example 1: A circular cylinder has base radius 7 cm and height 10 cm. Find the volume of the cylinder.

Solution: Here, r = 7 cm and h = 10 cm

Volume of the cylinder = πr2h = 22/7 × 7 × 7 × 10 = 1540 cm3

Example 2: The diameter of a cylinder is 40 cm and the height of the cylinder is 14 cm. Find the volume of the cylinder.

Solution: Given, diameter = 40 cm

Radius (r) = Diameter/2 = 40/2 = 20 cm

Height (h) = 14 cm

Volume of the cylinder = πr2h

= 22/7 × 20 × 20 × 14

= 22 × 800 = 17600 cm3

Example 3: A cylindrical water tank has the diameter of 7 m and height 5 m. How many litres of water can be stored in the tank?

Solution: Given, the diameter of the cylindrical water tank = 7 cm

Radius of the water tank = 7/2 = 3.5 m

Height of the water tank = 5 m

Volume of water in the tank = πr2h = 22/7 × 3.5 × 3.5 × 5 = 192.5 m3

1 m3 = 1000 litres

192.5 m3 = 192.5 × 1000 = 192500 litres

Hence, 192500 litres of water can be stored in the tank.

Example 4: The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 7 :

3. Find the ratio of their volumes.

Solution: Let the radii of the first and the second cylinder be 2k and 3k, respectively.

Again, let the heights of the first and the second cylinder be 7p and 3p, respectively.

Volume of the first cylinder (V1) = πr2h = π(2k)2 × 7p = 28πpk2

Volume of the second cylinder (V2) = πr2h = π(3k)2 × 3p = 27πpk2

Therefore, V1/ V2 = 28πpk2/27πpk2

V1 : V2 = 28 : 27

Hence, ratio of their volumes is 28 : 27.