A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3 from the base, then the volumes of the resulting cone and frustum are in the ratio

Options

A. `1:3`
B. `8:19`
C. `1:4`
D. `1:7`

Answer

B

Explanation

Volume of the original cone 'V' `=(pir^2h)/3`
Height of the smaller cone =2h/3
and radius `=(2r)/3("from similar" Delta's)`
Voume of smaller cone
`=1/3pi((2r)/3)^2(2h)/3=8/81pir^2h=(8V)/27`
`("Volume of smaller cone")/("Volume of frustum")=(8V//27)/(V-8V//27)=8/19`