Question

For the cube, $x$ represents a positive whole number. Find the value of $x$ such that the volume of the cube and 6 times the area of one of its faces have the same value.

Short answer

The length of the side of cube is $x=6$.

Step-by-step solution

Step 1. Volume of cube and area of square.

The volume of cube is $V={\left(side\right)}^3$and the area of base of the cube is$V={\left(side\right)}^3$

Step 2. Write the equation for the given statement.

The side of cube is $x$.

It is given that the volume of cube and 6 times the area of one of its faces have the same value.

Therefore, the required equation will be:

$x^3=6x^2$.

Step 3. Simplify the equation.

$\begin{array}{l}\frac{x^3}{x^2}=\frac{6x^2}{x^2}\\ x=6\end{array}$

The length of the side of cube is $x=6$.