Question

A cylinder and a cone have the same volume. The cylinder has radius x and height y . The cone has radius 1/2x . Find the height of the cone in terms of y .

Answer 1

height = 1/4y

Explanation:

V(cylinder) = πr²h

V(cone) = πr²h ÷ 3

V(cyl) = πx²y

V(cone) = π(1/2x)²y which simplifies to be πx²y ÷ 4

πx²y = πx²y ÷ 4

if you divide each side by πx² you get:

y = y/4

height is 1/4y