Question

Find the volume of a cubical box whose surface area is $486c{m}^2$.

Answer 1

We know that surface area of cube is $6l^2$.

It is given that the surface area of cube is $486$ cm${}^2$, therefore,

$486=6l^2\Rightarrow l^2=\frac{486}{6}\Rightarrow l^2=81\Rightarrow l=\sqrt{81}\Rightarrow l=9$

Now, the volume of the cube is $l^3$, therefore, the volume with length $l=9$ is:

$V=9^3=729$

Hence, the volume of the cube is $729$ cm${}^3$.