The difference of the square of the height and the square of the base of a right circular cone of slant height 10 cm is 28cm, then the volume of the cone will be

Options

A. `43pi c c`
B. `54 pi c c`
C. `72pi c c`
D. `96pi c c`

Explanation

Let the height of the right circular cone h cm and the radius of the base be r cm. The slant height of the cone is 10 cm .
`therefore h^2+r^2=(10)^2 or , h^2+r^2=100`................(1)
Again , `h^2-r^2=28`...................(2)
Adding (1) and (2) we get, `2h^2=128 or , 64 or , h=8`
`r^2=100-h^2=100-64=36`.
`therefore` the volume of the cone `=(1)/(3) xx pi xx 36 xx 8 c c =96 pi c c`.
`therefore` (d) is correct.