The ratio of the radius of the base of a right circular cone and its height is `3:7`, The volume of the cone is 528c c . Fin the diameter of the cone.

Explanation

Let the radius of the right circular cone and its height be 3x cm and 7x cm .
`therefore` the volume of the cone `=(1)/(3)pi (3x)^2.7x` cubic - unit.
As per question , `(1)/(3)pi (3x)^2.7x=528 or , (1)/(3)pi xx 9x^2.7x=528 or , (1)/(3)xx(22)/(7)xx63x^3=528 or , x^3=(528xx3xx7)/(22xx63)or , x^3=8 or , x=2`
`therefore` the radius of the cone `=3xx2cm=6cm`
`therefore` the diameter of the cone `2xx6cm=12cm`
Hence the diameter of the cone `=12cm`.