Question

If a cone and cylinder have congruent bases and equal altitudes, then the volume of the cylinder is:
A. three times of the volume of the cone
B. one-half the volume of the cone
C. equal to the volume of the cone
D. one-third the volume of the cone

Answer 1

Answer:  A. three times of the volume of the cone

Explanation:

The volumes of each solid are:

• volume of cone = (1/3)*pi*r^2*h
• volume of cylinder = pi*r^2*h

Notice that each formula involves pi*r^2*h. The only difference is that the cone has 1/3 up front. So we could effectively say:

• volume of cone = (1/3)*(volume of cylinder)

assuming the cone and cylinder have the same radius and height. Rearranging that last formula gets us:

• volume of cylinder = 3*(volume of cone)

Three identical cones take up the same amount of space as one cylinder.