If keeping the length of radius of a right circular cone fixed , the height of it is increased by 2 times , then the volume of cone will by increased by

Options

A. `100%`
B. `200%`
C. `300%`
D. `400%`

Explanation

Let the radius of the right circular cone be r unit and height is h unit .
`therefore` if the volume of the cone be V cubic - unit , then `V=(1)/(3)pi r^2h`
Now , if the height of the cone be doubled keeping the radius of it fixed, then the new volume of the cone `V_(1)=(1)/(3)pi r^2(2h)=2.(1)/(3)pi r^2h=2V....(1)`
So the volume increases `=(V_1-V)` cubic - unit `=(2V-V)` cubic unit `=V` cubic - unit.
Hence the percent of the increment in volume `=(V)/(V)xx100%[("increment in volume")/("primary volume")xx100%]=100%`
`therefore` (a) is correct.