Question

Find the volume of the cubical box whose surface area is 486 $c{m}^2$.

Answer 1

Hint: Here, we will first find the value of the edge with the given surface area and then the Volume of the cubical box can be calculated as $a^3$.
Given,
Surface area of cubical box is 486 $c{m}^2$ i.e.., $6a^2=486$ where ‘a’ is the edge .Now let us find the value of the edge i.e..,
$$\begin{gathered} \Rightarrow 6a^2=486 \\ \Rightarrow a^2=\frac{486}{6} \\ \Rightarrow a^2=81 \\ \Rightarrow a=9 \end{gathered}$$
Hence, the obtained value of edge (a) is 9 cm. As we know that the volume of the cubical box is $a^3$.
Therefore, substituting the obtained value of ‘a’ we get
$\Rightarrow a^3=9^3=729\text{ c}{\text{m}}^3$
Hence, the volume of the cubical box is 729 $\text{c}{\text{m}}^{\text{3}}$.
Note: Since, all the sides of a cubical box are equal. The volume of the cube is calculated by multiplying the value of a side 3 times i.e.., V=side*side*side.