Question

The edge of one is 4cm longer than the edge of a second cube.The volume of the cubes differ by 316m square. Find the length of each cube

Anyone that answers I will mark as brilliant

Answer 1

The sides are 3 and 7 cm long.

Explanation:

Let the lengths be x and x+4 cm, then

(x + 4)^3 - x^3 = 316

x^3 + 12x^2 + 48x + 64 - x^3 = 316

12x^2 + 48x + 64 - 316 = 0

12x^2 + 48x - 252 = 0

12(x^2 + 4x - 21) = 0

12(x + 7)(x - 3) = 0

x = -7, 3

So one cube has side of length 3 cm.

The other has side 3+4 = 7 cm.