Question

Adam built a toy box for his children’s wooden blocks.

A. If the inside dimensions of the box are 18 inches by 12 inches by 6 inches, what is the maximum number of 2-inch wooden cubes that will fit in the toy box?

B. What if Adam had built the box 16 inches by 9 inches by 9 inches? What is the maximum number of 2-inch wooden cubes that would fit in this size box?

Answer 1

A. 162

B. 128

Explanation:

We have wooden cubes of 2 in of side.

A. If the box is 18 x 12 x 6 in., in the base (18 x 12), we can fit 54 cubes:

`(18)/(2)\cdot (12)/(2)=9\cdot 6=54`

As the height is 6 in, we can fit 6/2=3 layers of 54 cubes in the box, se we can fit 162 cubes:

`B=3\cdot54=162`

B. If we have a box with measures 16 x 9 x 9 in., and the base is 16x9 in, we can fit (16/2)*(9/2)=8*4=32 cubes per layer.

Note that in the 9 in side we can only put 4, as we need 10 in to fit 5 cubes (we can not cut them).

In the same way, as we have 9 in of height, we can fit 4 layers of 32 cubes, so this is a total of 128 cubes:

`B=4\cdot32=128`