A cylinder and a cone have the same volume. The cylinder has radius x and height y. The cone has radius 12x. Find the height of the cone in terms of y.

Answer 1

The cylinder has radius = x and height = y.

Its volume is

V1 = πx²y

The cone has radius = 12x and an unknown height = h.

Its volume is

V2 = (1/3)π(12x)²h = (1/3)π(144x²)h = 48πx²h

The two volumes are equal. Therefore

48πx²h = πx²y

Divide each side by πx² .

48h = y

h = y/48

Answer: h = y/48.

Check the answer.

V1 = πx²y

V2 = 48πx²h = 48πx²(y/48) = πx²y

V1 = V2, so the answer is correct.