The radius of right circular cone A is `(1)/(5)` of the radius of right circular cone B, and the height circular cone A is `(1)/(4)` of the height of right circular cone B. What is the ratio of the volume of right circular cone A to the colume of right circular cone B ?

Options

A. `(1)/(16)`
B. `(1)/(25)`
C. `(1)/(64)`
D. `(1)/(100)`

Answer

D

Explanation

The volume of a right circular cone is `(1)/(3)pi r^(2)h`. If the radius of cone B is x and the height is y, then the area is `(1)/(3)pi x^(2)y`. The radius of cone. A will be `(1)/(5)x` and the height will be `(1)/(4)y`, so the volume is `(1)/(3)pi ((1)/(5)x)^(2)((1)/(4)y)=(1)/(300)pi x^(2)y`. The ratio of the volume of cone A to that cone B is therefore
`((1)/(300)pi x^(2)y)/((1)/(3)pi x^(2)y)=(1)/(300)div(1)/(3)=(1)/(100)`