Question

13 points. A cylinder and a cone have the same volume. The cylinder has radius x and height y. The cone has radius 4x. Find the height of the cone in terms of y.

Answer 1

Remark
General Formulas
Volume of a cylinder = pi r^2 h
Volume of a cone = 1/3 pi r^2 h

Givens
Cylinder
Cylinder radius = x
Cylinder height = y

Cone
Cone Radius = 4x
height = ???

Solution
The volumes are the same, so you can just equate the right side of both equations to each other.

Volume Cylinder = Volume Cone
pi * x^2 * y = 1/3 pi * (4x)^ h Divide both sides by pi
x^2 * y = 1/3 * 16x^2 * h Divide both sides by x^2
y= 1/3 * 16 * h Multiply by 3
3 *y = 16 * h Divide by 16
(3/16)y = h <<<< Answer.

This is a very handy problem to study especially if you plan on taking physics.