A solid right circular cylinder is melted down and recast into a right circular cone with the same base radius. If the cylinder's height is h, what is the height of the cone?
Show answer & explanation
Correct answer: A
Explanation
Height of the cylinder = h
Base radius of the cylinder and the cone is the same = r
According to the formula:
Volume of the cylinder = πr²h
Volume of the cone = (1/3)πr²H
Volume of the cylinder = Volume of the cone
πr²h = (1/3)πr²H
πr² cancels out
h = H/3
H = 3h
Height of the cone = 3h