Question

The total surface area of a cube is 1350 sq. m. Find its volume.

Answer 1

Hint: In order to solve this question, we will first calculate the side of the cube from the given total surface area of a cube, which is equal to $6{{a}^{2}}$ and then we will find the required volume of cube by the formula for volume of cube = ${{a}^{3}}$, where a represents the side of the cube.

Complete step-by-step answer:
In this question, we have been given that the total surface area of a cube is 1350 sq. m and we have been asked to find the volume of the cube. Now, we will first draw the figure according to the given question, as given below.

Now, let us consider the side of the cube as a metre. And we know that the total surface area of a cube is given by $6{{\left( side \right)}^{2}}$. So, we can say the total surface area of the cube is equal to $6{{a}^{2}}$. Therefore, we can write as,
$6{{a}^{2}}=1350$
Now, we will simplify it to get the value of a. So, we can write,
$\begin{align}
  & {{a}^{2}}=\dfrac{1350}{6} \\
 & \Rightarrow {{a}^{2}}=225 \\
\end{align}$
Now, we know that we can express 225 as ${{15}^{2}}$. So, we can say that,
${{a}^{2}}={{15}^{2}}$
And further we can say a = 15 m.
Now, we have been asked to find the volume of a cube. And we know that the volume of a cube is given by ${{\left( side \right)}^{3}}$. So, we can say that,
Volume of cube = ${{a}^{3}}$
Now, we will substitute the value of a in this. So, we get,
Volume of cube = ${{15}^{3}}$
And we can further write it as,
Volume of cube = $3375{{m}^{3}}$
Hence, we can say that, if the total surface area of a cube is 1350 sq. m, then the volume of the cube will be 3375 cu. m.

Note: The possible mistakes that can be made while solving this question is that we can write the incorrect formula of total surface area and volume of a cube, which can result in an incorrect answer. Similarly, there are chances of making calculation mistakes too. So, one should be thorough with the formulas and be careful.