Question

A cylinder has a diameter that is twice it’s height. Another cylinder has a height that is twice it’s diameter. Which cylinder has a greater volume?

Answer 1

Cylinder on the left has 2 times the volume

Explanation:

Volume of the cylinder on the left

V = pi * r^2 h

The radius is 1/2 the diameter, so

r = 2x/2 = x

r =x and h =x

Substituting in

V = pi * x^2 *x

V = pi x^3

Volume of the cylinder on the right

V = pi * r^2 h

The radius is 1/2 the diameter, so

r =x/2 and h =2x

Substituting in

V = pi * (x/2)^2 *2x

V = pi x^2/4 *2x

V= pi x^3 *1/2

V = 1/2 pi x^3

The volume of the cylinder on the right is 1/2 the volume of the cylinder on the left.

Cylinder on the left has 2 times the volume