Find the volume of a cone of height 8 centimeters and base radius 6 centimeters. This cone is sliced by a plane that is parallel to the base and 2 centimeters from it. Find the volumes of the two resulting solids. One is a cone, while the other is called a frustrum.

Answer 1

the cones are similar, with the smaller altitude 6/8 = 3/4 the altitude of the larger
So the volume of the smaller is (3/4)^3 times that of the larger
The larger cone has volume 1/3 π * 6^2 * 8 = 96π
The smaller cone has volume 27/64 * 96π = 81π/2
The frustrum has volume 96π - 81π/2 =111π/2