Question

A rectangular prism has a volume of 384 cm cubed the width is twice the height and the length is 3 times the height what are the dimensions of the prism?

Answer 1

V = L * W * H
Let H be the height.
Let L = 3 H L is the length
Let W = 2H W is the width.

V = H *3H * 2H
V = 6 H^2

V = 384 cm^3
384 cm^3 = 6H^3 Divide both sides by 6
384 / 6 = H^3
64 = H^3 Take the cube root of both sides.
Cube Root 64 = H
H = 4 cm

L = 3 * 4 = 12
W = 2*4 = 8
H = 4cm <<<<<< answer.