It takes one kilogram of metal to make a certain solid cube. What mass of metal is needed to make a cube of the same metal whose edges are twice as long as the first? Explain your answer.

8 kg

Assuming the new cube will also be solid, let's work the problem 1 dimension at a time. 1. Take your original cube and create a duplicate. Now weld those duplicate cubes together to make a box that's twice as wide as the original cube, but has the same depth and height as the original cube. It's obvious that this new box has twice the mass as the original cube.

2. Take the box created in step 1 above and duplicate it again. Now weld those two boxes together to get a square box that has double the width and depth as the original cube, but has the same height. It's obvious that this new box has twice the mass as the box created in step 1 which is turn has twice the mass as the original cube. So it has 2 * 2 = 4 times the mass of the original cube.

3. Finally, take the box created in step 2 above and duplicate it once more. Then stack those two boxes on top of each other to create a cube. Once again, it has twice the mass of the box in step 2, so it has 4 * 2 = 8 times the mass of the original cube.

Since the original cube has a mass of 1 kg, the new cube that's twice as long in all dimensions has 8 * 1 kg = 8 kg of mass.