Question

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 5 inches. The height of the cone is 15 inches.

Use π = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Answer 1

cone is 1/3 volume of similar cylinder

since they have same diameter, the bases are the same
cone has height 3 times as high as cylinder, this makes volumes equal.

\[V_{cone} =\frac{1}{3} \pi r^2 (3h) = \pi r^2 h = V_{cylinder}\]
if h = 5