Question

If the base radius and the height of a right circular cone are increased by 20%, then the percentage increase in volume is approximately

Options

• 60

•  68

• 73

• 78

Answer 1

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume of cone = `1/3 pi r^2h`

= V

It is given that the base radius and the height are increased by 20%. So now the base radius is ‘1.2r’ and the height is ‘1.2h’.

So,

The volume of the modified cone =`1/3 pi(1.2r)^2(1.2h)` 

`=1.728/3 pir^2 h`

= 1.728 V

Hence the percentage increase in the volume of the cone is 72.8%, which is approximately equal to 73%.