Question

Jan built a cube from unit cubes (each 1 by 1 by 1 unit). Ken took this cube apart,and used the unit cubes to build a rectangular solid that was the same height asJan's cube but 2 units greater in width and 2 units less in length. Ken had 24 unit cubes left over. How many unit cubes did Ken use to build his figure?

Answer 1

solve

x^3 - x(x+2)(x-2) = 24
x^3 - x(x^2-4) = 24
x^3 - x^3 + 4x = 24
4x=24
x=8

So Jan used 8^3 or 515 cubes
Ken used 24 less or 488 cubes

check:
original:
8^3 = 512
Ken's cube = 8 x 6 x 10 = 480
512-480=24

Answer 2

Thanks much.

Answer 3

The answer is X=6, not X=8. Ken's cube was 6 x 4 x 8 = 192, Jan's was 6 x 6 x 6 = 216. 216 - 192 = 24.