A right circular cone of height h is cut by a plane parallel to the base and at a distance h/3
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 : 4
- 1 : 7
- 8 : 19
- 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.