Question

If the surface area of a cube is 384 square feet,what is its volume?

Answer 1

Volume `= 512` cubic feet

Explanation:

A cube has `6` faces all with equal area.
If the total surface area of the cube is `384` sq.ft.
then each face has an area of `384div6=64` sq.ft.

Each face of a cube is a square and if we denote the length of an edge as `E`
then the area of a face (in this case `64` sq.ft.) is equal to `E^2`
`color(white)("XXX")E^2=64` sq.ft.
`color(white)("XXX")rarr E = 8` sq.ft.

The volume of a cube with edges of length `E` is `E^3`.
In this case `"Volume" = E^3 = 8^3 = 512` sq.ft.