Question

The length of the side is 3.9ft. Find the surface area of a cube.
\[
  A.\;\;\;\;\;41.82{\text{ }}f{t^2} \\
  B.\;\;\;\;\;94.16{\text{ }}f{t^2} \\
  C.\;\;\;\;\;91.26{\text{ }}f{t^2} \\
  D.\;\;\;\;\;40.41{\text{ }}f{t^2} \\
 \]

Answer 1

Hint: We know that a cube has 6 square faces and the surface area is the sum of the area of all the square faces. We can find the surface area using the equation surface area ${\text{ = 6}}{{\text{a}}^{\text{2}}}$, where a is the length of the side.

Complete step by step solution: We are provided with the length of the side of a cube, a = 3.9ft
A cube has 6 square surfaces and each of the square surfaces has an area equal to $\text{a}^{2}$.
The total surface area is obtained by adding the area of 6 square faces. As all the squares are identical, the total surface area is given by $6\text{a}^{2}$.
Now we put the value of ‘a’ into the equation,
${\text{ = 6}}{{\text{a}}^{\text{2}}}{\text{ = 6}}{\left( {{\text{3}}{\text{.9}}} \right)^{\text{2}}}$
After simplification we get,
$\text{ = 6 } \times {\text{15.21 = 91}}{\text{.26f}}{{\text{t}}^{\text{2}}}$
Therefore, the surface area is 91.26 $\text{ft}^{2}$

So, the correct answer is option C.

Note: In this question we were asked to find the surface area of a cube, and we were provided with the length of the side, the format of question can be changed and it can be asked to find the length of the side is Surface area of the cube is given. Or else we can also be provided with the surface area of a cube and we need to find the volume of the cube, so we first find the length of the cube from the given surface area and then we use the formula of volume of cube i.e. \[{\text{V = }}{{\text{a}}^{\text{3}}}\] to get the desired result.