a cube has a square hole all the way through it. if the volume of wood used to construct the cube is 3072 mm^3, what are the dimensions of the cube and the hole?
+128460
The volume of the solid cube is given by :
(4x)^3 = 3072 mm^3 simplify
64x^3 = 3072 divide both sides by 64
x^3 = 48 take the cube root of both sides
x = ∛48 mm = 2∛6 mm
So each side of the cube is just 4x = 4 ( 2∛6 mm ) = 8 ∛6 mm
And the volume of the square hole is just the dimensions 2x * 2x * 4x
(2x)^2 * 4x = 16 x^3 = 16 ( ∛48)^3 = 16 * 48 = 768 mm^3
