Question

A cube has a volume of `1/64` cubic meter. How do you complete the explanation for finding the length of each side of the cube?

Answer 1

`color(green)("Length of each side of the cube " = a = (1/4) " m"`

Explanation:

`"Volume of a cube " V = a^3 " where a is the side "`

`"Given " V = 1/64 " m"`

`:. V = 1/64 = a^3`

`a = root 3 (1/64)`

`a = (1/64)^(1/3)`

`a = (1 / (4 * 4 * 4))^(1/3)`

`a = ((1/4)^3)^(1/3)`

`a = (1/4)^(cancel3 * cancel(1/3))`

`color(green)(a = 1/4 " m"`

Answer 2

The length of each side of a cube is equal

Let `l` be the length of one side of the cube
then the volume `V=l times l times l` or `V=l^3`

Since the volume of the cube is `1/64`, then `1/64=l^3`
Therefore, `l=root(3)(1/64` so `l=1/4`