Question

If volume of a cube is $64c{{m}^{3}}$, find its surface area

Answer 1

- Hint: In this question we have to find out the surface area of a cube. So, it is important to know about a cube. A cube is a three-dimensional object in which length, breadth and height are equal in length.it has six equal surfaces which are in a square shape. The area of the square is given by \[A={{\left( a \right)}^{2}}\]where $a$ is the length of the side of a square, so we have to find the length of the side. Once we find the length of the side of the square, we get the area of the square. As we know that there are six equal surfaces in a square shape so the total surface area is six times the area of one surface. The length of the side of a square can be found from the information given in the question that the volume of the cube is $64c{{m}^{3}}$. The volume of the cube is given by $V={{(a)}^{3}}$.

Complete step-by-step solution -
Let us suppose that volume of the cube is denoted by $V$. So, from question we have
$V=64c{{m}^{3}}$
As we know that the volume of cube is given by $V={{(a)}^{3}}$, where $a$is the length of the side of cube, so we can write
\[\begin{align}
  & {{a}^{3}}=64c{{m}^{3}} \\
 & \Rightarrow \left( a \right)\left( a \right)\left( a \right)=\left( 4cm \right)\left( 4cm \right)\left( 4cm \right) \\
\end{align}\]
On comparing we can write
$a=4cm$,
Hence, we get the side of the cube.
Now as we know area of a square
\[A={{\left( a \right)}^{2}}\]
So, area of one surface of cube
$\begin{align}
  & A=\left( 4cm \right)\left( 4cm \right) \\
 & A=16c{{m}^{2}}------(1) \\
\end{align}$
Now we have to find the surface area of the cube, as we know that there are six equal surfaces in a cube, three sides are visible and three others are not visible. See figure.
Suppose surface area is denoted by $S$, so we can write
$S=6A$
Putting the value of $A$from $(1)$we get the surface area of cube
$\begin{align}
  & S=6(16c{{m}^{2}}) \\
 & \Rightarrow S=96c{{m}^{2}} \\
\end{align}$
Hence surface area is $96c{{m}^{2}}$

Note: In such a type of question, it is important to draw the figure so as to visualize the condition, what is given and what is to be found. Also take care the unit, as volume is a three dimensional figure so length is multiplied three times so its unit is $c{{m}^{3}}$and surface is a two dimensional figure so length is multiplied two times so its unit is $c{{m}^{2}}$.