A square pyramid has a base edge of 32 inches and an altitude of 1 foot. A square pyramid whose altitude is one-fourth of the original altitude is cut away at the apex of the original pyramid. The volume of the remaining frustum is what fractional part of the volume of the original pyramid?
The "new" pyramid and the original pyramid are similar figures
The scale factor of the "new" pyramid to the original pyramid = 1/4
Let the volume of the original pyramid be = V
The volume of the "new" pyramid = V * (1/4)^3 = V / 64
The volume of the remaining frustum = V - V/64 = (63/64)V
So the volume of the frustum is (63/64) of volume of the original pyramid