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.

Answer 1

Volume of cube = s^3

Volume of cone = (1/3)Ah

Cube:

V = s^3 = (2 in.)^3 = 8 in.^3

Cone:

V = (1/3) *pi * (3 in.)^2 * h = 8 in.^3

pi * 9h = 24 in.

h = 24/(9pi) in.

h = 8/(3pi) in.

h is approximately equal to 0.849 in.

Answer: The height is (8/3)pi inches which is approximately 0.849 inches