Question

A cubic crate with an edge length of 16 feet will be used to contain cubic wooden boxes. Each wooden box has an edge length of 4 feet. How many wooden boxes can the crate contain?

Answer 1

The side length of the cubic crate = 16 feet

The cubic crate will contain cubic wooden boxes, each box of side length = 4 feet

We have to determine the number of boxes which can be contained in a crate.

Since, Volume of a cube with side 'a' is given by =
`a^3`.

Number of cubic wooden boxes = Volume of cubic crate
`/` Volume of a cubic wooden box

So, volume of cubic crate =
`(side)^3` =
`(16)^3` = 4096

Volume of each cubic wooden box=
`(side)^3` =
`(4)^3` = 64

So, number of cubic wooden box contained in a crate =
`(4096)/(64)` = 64

Therefore, 64 cubic wooden boxes are contained in a crate.