If the height of a right circular cone be increased by `10%` keeping its radius fixed , then the volume of the cone will be

Options

A. `5%`
B. `10%`
C. `15%`
D. `20%`

Explanation

Let the radius of the base of a right circular cone be r unit and its height be he unit .
`therefore` if the volume of the cone V cubic- unit , then `V=(1)/(3)pi r^2h`....................(i)
Now , if the height be increase by `10%` then the height will be
`(h+hxx(10)/(100))"unit"=(h+(h)/(10))"unit"=(11h)/(10)"unit"`.
Then the volume of the cone `=(1)/(3)pi r^2xx(11h)/(10)"cubic-unit"=(11)/(10)xx(1)/(3)pi r^2h"cubic - unit"`.
`=(11V)/(10)"cubic-unit"`
`therefore` the icrement of volume `=((11V)/(10)-V)"cubic-unit"=(V)/(10)"cubic- unit"`
So , the percent of increment of volume ` ((v)/(10))/(V)xx100%=10%`
`therefore` (b) is correct.