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.

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.