Question

If the area of one face of the cube is $1.5$ times its perimeter, the volume $\left(\text{in}{\text{cm}}^3\right)$ of the cube is:

• A. $125$
• B. $144$
• C. $216$
• D. $312$

Answer 1

The correct option is C $216$

Let each side of the cube be $a$.

We know, area of one face of a cube $=a^2$

and perimeter of a cube $=4a$.

Now, according to the statement,
$\therefore a^2=1.5\times 4a$

$\Rightarrow a=6$.

Then, the volume of the cube $=a^3$

$=6^3=216c{m}^3$.

Hence, option $C$ is correct.