Volume of a cylinder

Volume of a cylinder

The volume of a cylinder is obtained by multiplying its base area by height.

The base area of a cylinder is circular and it is obtained by using the following formula:

Area of circle = π × diameter × diameter/4

= πd²/4

= πr²

Thus, Volume of a cylinder = Area of a circle × height

Therefore, the volume of cylinder = πr²h.

Example 1

Find the volume of a cylinder with diameter 28 cm and height 50 cm.

Solution

Using the diameter:

Volume of a cylinder = πd²h/4

= 22/7 × 28 cm × 28 cm/4 × 50 cm

= 30,800 cm³

Therefore, the volume of the cylinder is 30,800 cm³

Alternatively, using the radius:

The volume of the cylinder = πr²h

= 22/7 × 14 cm × 14 cm × 50 cm

= 30,800 cm³

Therefore, the volume of the cylinder is 30,800 cm³

Example 2

The volume of a cylinder is 41,580 cm³. If its height is 30 cm, find its radius.

Solution

Volume of a cylinder = πr²h

41,580 cm³ = 22/7 × r² × 30 cm

Multiply by 7 both sides of the equation:

7 × 41,580 cm³ = 22 × r² × 30 cm

291,060 cm³ = 660 cm × r²

Divide both sides by 660.

291,060 cm³ / 660 cm = 660 cm × r² / 660 cm

r² = 441 cm²

Find the square root on both sides:

Therefore, the radius of the cylinder is 21 cm.