Question

The surface area of a cube is 96 ft.² find the volume of a cube

Answer 1

A cube has 6 faces. Those 6 faces are squares with side s

Now, the area of one of these squares is:

`s^2`

Thereby, the surface area of the cube would be:

`6\cdot s^2`

Since we know the surface area of the cube, we can calculate the measurement of its sides:

`\begin{gathered} 96=6s^2 \\ \rightarrow s^2=(96)/(6)\rightarrow s^2=16\rightarrow s=\sqrt[]{16} \\ \Rightarrow s=4 \end{gathered}`

Since we know that the volume of a cube is equal to

`s^3`

We can calculate the volume of the cube:

`\begin{gathered} V=4^{3^{}} \\ \Rightarrow V=64 \end{gathered}`

This way, we can conclude that the volume of the cube is 64 cubic feet

(Answer: Option 1)