Question

Janine can use up to 150 one-inch blocks to build a solid, cube-shaped model. What are the dimensions of the possible models that she can build? How many blocks would Janine use for each model? Explain.

Answer 1

A solid cube with integer side length n (in inches) made from 1-inch cubes uses n^3 blocks. With at most 150 blocks we need n^3 ≤ 150.

1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125, while 6^3 = 216 > 150.

So possible cubes are:
- 1×1×1 using 1 block
- 2×2×2 using 8 blocks
- 3×3×3 using 27 blocks
- 4×4×4 using 64 blocks
- 5×5×5 using 125 blocks