Question

If the total surface area of a cube is $54x^2$, find its lateral surface.

Answer 1

Step 1: Finding the square of edge of cube

Let the edge of the cube be $a$.

Then, total surface area of the cube $=6a^2$.

Given that, the total surface area of a cube is $54x^2$.

Equating the formula and the given value, we get,

$\begin{array}{rcl}6a^2& =& 54x^2\\ & \Rightarrow & a^2=9x^2\end{array}$

Step 2: Finding the lateral surface of the cube

We know, that the lateral surface of the cube is $4a^2$

Substituting the value of $a^2$ in the above expression, we will get,

$\begin{array}{rcl}LSA& =& 4\left(9x^2\right)\\ & \Rightarrow & LSA=36x^2\end{array}$

Hence, the lateral surface area of the cube is $36x^2$.