A prototype engineer models a container as a cube and a cylinder, both with the same height and the cylinder's radius being half the cube's side. What is the ratio of their volumes?
Show answer & explanation
Correct answer: D
Explanation
Given:
Side of cube = a
Height of cylinder = a
Radius of cylinder = a/2
By formula:
Volume of cube = a³
Volume of cylinder = πr²h
Volume of cube = a³
Volume of cylinder = π(a/2)² × a = πa³/4
Ratio (cube : cylinder) = a³ : πa³/4 = 4 : π