Question

The length of the side is 3.9 ft. Find the surface area of a cube.
$41.82{\text{ f}}{{\text{t}}^2}$
$94.16{\text{ f}}{{\text{t}}^2}$
$91.26{\text{ f}}{{\text{t}}^2}$
$40.41{\text{ f}}{{\text{t}}^2}$

Answer 1

Hint:
It is known to us that a cube has 6 square faces and the surface area of the cube is the sum of the area of all the square faces. Hence, we can find the surface area of the cube by using the equation ${\text{Surface Area}} = 6{a^2}$. Here, ‘a’ is the length of the side of the cube.

Complete step by step solution:
Let us begin by considering what is given to us in the question. It is given that the side of the cube is 3.9 ft.
$ \Rightarrow a = 3.9{\text{ ft}}$
It is known that the total surface area of the cube is obtained by adding the area of all the 6 square faces. As all the squares are identical, the required total surface area is given by;
${\text{Surface Area}} = 6{a^2}$
Substituting the values into the formula, we get;
${\text{Surface Area}} = 6{\left( {3.9} \right)^2}$
Let us now simplify the obtained expression to find the required area.
$
  {\text{Surface Area}} = 6 \times 15.21{\text{ }}f{t^2} \\
   = 91.26{\text{ }}f{t^2} \\
 $

Hence, the required surface area of the cube is $91.26{\text{ f}}{{\text{t}}^2}$, which is option (c).

Note:
In the given question, it was required to find the surface area of a cube, and only the length of the side was being given to us. But, the format of the question can also be changed sometimes and you can be given the surface area and will be asked to calculate the side of the cube. Or making it tough, it can be in a way where the surface area of the cube will be given and you can be asked to calculate the volume of the cube. In this case we need to first find the length of the cube and then apply it in the formula for the volume of the cube, given by \[{\text{V}} = {a^3}\] to find the required value.