If the height and the area of base of a right circular cone be increased by 4 times, then how many times the volume of the cone will be increased ?

Explanation

Let the initial radius of the base and height of the cone be r unit and h unit respectively. Now , if the area of the base be increased by 4 times , let the radius of the base will be `r_1` unit.
`therefore pi r_(1)^(2)=4pi r^2rArr r_(1)^(2)=4r^2rArr r_(1)^(2)=(2r)^2rArr r_1 = 2r`
If the initial volume of the cone be V cubic - unit , and the volume after increment be `V_1` cubic - unit , the `V=(1)/(3)pi r^2h and V_1=(1)/(3)pi. (2r)^2.4h=16.(1)/(3)pi r^2h=16V[because V=(1)/(3)pi r^2h]`
Hence the volume of the cone will be 16 times of its initial volume , if its height and area of base is increased by 4 times.