Question

what is the maximum number of cubes with side lengths of 1/2 cm that can fit into a right rectangular prism with base dimensions of 12 1/2 cm by 8 1/2cm and a height of 9 1/2cm?

Answer 1

8075.

Explanation:

Volume of the prism

= 12 1/2 * 8 1/2 * 9 1/2

= 25/2 * 17 / 2 * 19/2

= 8075/8 cm^3

The volume of the small cubes = (1/2)^3 = 1/8 cm^3

So the number required = 8075 / 8 / 1/8

= 8075*8 / 8

= 8075.