Question

A plastic circular cone with a volume of x cubic centimeters is sliced horizontally into two shapes. If the height and radius of the smaller cone is half the height and radius of the original cone, which expression represents the volume of the other piece in cubic centimeters?

Answer 1

For the original cone:
V = pi*h*r^2 = x
The upper half of the cone has half the height and half the radius of the original cone of volume x, so its volume is calculated as:
V = pi*(h/2)*(r/2)^2 = (1/8)*pi*h*r^2 = x/8

Therefore the volume of the other piece (the frustum) is x - (x/8) = 7x/8 cubic centimeters.