Question

Calculate the surface area of a cube of edge $4\,cm$? What is the volume?

Answer 1

Hint: In order to calculate the surface area and volume of a cube, we should know first what is a cube. A cube is a three-dimensional figure, either solid or hollow, that consists of six equal square sides. To find the surface area and volume of the cube just substitute the value of edge given, in the formula of surface area and volume we already know.

Complete step by step answer:
We are given a cube with an edge of $4\,cm$. From the formula of surface area, we know that: Surface Area $ = 6{a^2}$, where $a$ refers to the edge of the cube. So, substituting the value of edge $\left( a \right)= 4\,cm$ as given, and solving for surface area and we get:
$\text{Surface Area} = 6{a^2} \\
\Rightarrow \text{Surface Area}= 6{\left( 4 \right)^2} \\
\Rightarrow \text{Surface Area}= 6 \times 16 \\
\therefore \text{Surface Area}= 96c{m^2}$

Similarly, from the known formula of volume of a cube, we get: Volume$ = {a^3}$.
Substituting edge $\left( a \right)$$ = 4cm$, in the above formula of volume and on further solving, we get:
\[\text{Volume} = {a^3} \\
\Rightarrow \text{Volume}= {\left( 4 \right)^3} \\
\therefore \text{Volume}= 64\,c{m^3}\]

Hence, the surface area of a cube of edge $4\,cm$ is $96\,c{m^2}$ and volume is $64\,c{m^3}$.

Note:Surface area and volume area is calculated only for any three-dimensional geometrical shape, not for two dimensional because two dimensional objects only have area not any surface or volume. Surface area refers to the total area covered by the surface of the given object. It is measured in square units. Whereas, Volume is the amount of space occupied by any object. It is measured in cubic units.