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Find the volume of a cube, one face of which has an area of $64{m^2}$.

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Last updated date: 13th Jun 2024
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Answer
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Hint:
To find the volume we have to find the side of the cube. The area of one face is given to us and we can find the side from the area i.e.
\[ \Rightarrow A = {a^2}\]
Where $A$ is the area of one face of the cube and $a$ is the side of the cube. After that we will find the volume of a cube by formula given below:
$ \Rightarrow V = {a^3}$
Where $V$ is the volume of the cube and $a$ is the side of the cube.

Complete step by step solution:
Let us see what is given to us? We are given with the area of one face of a cube i.e.
$ \Rightarrow A = 64{m^2}$ ………(1)
We have to find the volume of a cube.
First of all, we will find the side of the cube. Now, as we know the cube consists of 6 faces and these 6 faces are square in shape. So, if we know the area of one face of a cube and we can find the side by applying the formula of area of square as follows
\[ \Rightarrow A = {a^2}\]
Put the value of $A$ from (1), we get,
\[ \Rightarrow 64 = {a^2}\]
By taking square root on both sides we get,
\[ \Rightarrow \sqrt {64} = \sqrt {{a^2}} \]
Now, 64 can be expressed as square of 8 and we get,
\[ \Rightarrow \sqrt {{{\left( 8 \right)}^2}} = \sqrt {{a^2}} \]
By cancelling square with square root then we get,
$ \Rightarrow a = 8m$ ………….(2)
Now, we have the side of the cube and we can find the volume of a cube by formula i.e.
$ \Rightarrow V = {a^3}$
Put the value of $a$ from (2) and we get,
$ \Rightarrow V = {8^3}$
As the cube of a number is obtained by multiplying the number itself 3 times. So, we get,
$ \Rightarrow V = 8 \times 8 \times 8$
$ \Rightarrow V = 512{m^3}$

Therefore, the volume of the cube is $512{m^3}$.

Note:
If they had given the surface area of cube then we will find the side by the following formula;
$ \Rightarrow A = 6{a^2}$
Here, the area of one face of the cube is \[{a^2}\]. As it has 6 faces, we multiply \[{a^2}\] with 6 to get the total area of the cube.
If in the question they asked for the surface area of the cube then apply the above formula.