Alex has 512 cubes, with dimensions in feet (ft), like the one shown. He uses all the cubes to fill a box shaped like a larger rectangular prism. There are no gaps between the cubes.

A) First, find the volume of each cube:

V = s³

  = (1/2)³

  = 1/8 ft³

We have a total of 64 cubes, therefore the maximum volume will be:

Vmax = 64 · (1/8) = 8 ft³

B) The volume of a rectangular prism is given by:

V = w × l × h

Therefore any combination of w × l × h = Vmax = 8 will be fine.

Examples:

2 × 2 × 2

4 × 2 × 1

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w