Question

Mark packed 1 inch cubes into a box with a volume of 120 cubic inches. How many layers of 1-inch cubes did mark pack?

Answer 1

5 layers of smaller cube approximately.

Explanation:

We are given the following data in the question:

Volume of the bigger box = 120 cubic inches.

Side of smaller cube = 1 inch

Volume of smaller cube =
`side* side* side` =
`1* 1* 1` = 1 cubic inches.

Number of smaller cubes that can be fit into bigger box =
`(120)/(1)` = 120

If we assume that the bigger box is also a cube, then we can calculate the side of the bigger box

`120 = side* side* side`

`Side = \sqrt[3] {120}` = 4.932

Thus, the side of the bigger box is approximately equal to 5 inch.

Thus, approximately Mark can pack the smaller cubes into the bigger box by stacking 5 layers of smaller cubes. Now, each layer of smaller cubes contain approximately 25 cubes.

Answer 2

The number of layers of 1-inch cubes that Mark packed is determined by assuming that the larger box is also a cube.
120 = e³
The value of e from the equation is approximately 5. Thus, there are approximately 5 layers of 1-inch cubes.