Question

A solid gold cube with edge of 2" is melted down and recast as a cone with a 3" radius base. Find the height of the cone.

8/(9) pi
2pi
8/(3) pi

Answer 1

The volume of a cube is side length cubed, so it's 2^3 = 8

The volume of a cone is 1/3 * height * base area = 1/3 * h * pi * r^2

Since the amount of gold in the cube and cone are the same, we know 1/3 * h * pi * r^2 = 1/3 * h * pi * 3^2 = 8
So h * pi * 9 = 24
h*pi = 24/9 = 8/3
h = 8/(3*pi)

Answer 2

Thanks so much