A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3

• Mensuration

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 the frustum are in the ratio

1. 1 : 4
2. 1 : 7
3. 8 : 19
4. 1 : 3

Answer

Volume of original cone with height h = V = 1/3 πr²h

Height and radius of new cone = 2h/3 and 2r/3

Volume of new cone = 1/3 π(2r/3)²(2h/3) = 8V/27

Volume of frustum = (1 - 8/27) V = 19V/27

Ratio = 8/27 : 19/27 = 8 : 19

The correct option is C.