Question

If the total surface area is equal to the volume of a cube, then find the side of the cube.

Answer 1

Let $a$ be the side of the cube.

Then total surface area $=6a^2$ and its volume is $a^3$.

Then according to the problem ,

$a^3=6a^2$

or, $a^2(a-6)=0$

or, $a=6$ , as $a=0$ is not possible (side cannot be equal to zero)

So the side of the cube is of $6$ units.