Question

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

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 ${a^3}$.
Surface area of cubical box is 486 $c{m^2}$ i.e.., $6{a^2} = 486$ where ‘a’ is the edge .Now let us find the value of the edge i.e..,
$\Rightarrow 6{a^2} = 486 \\ \Rightarrow {a^2} = \frac{{486}}{6} \\ \Rightarrow {a^2} = 81 \\ \Rightarrow a = 9 \\$
Hence, the obtained value of edge (a) is 9 cm. As we know that the volume of the cubical box is ${a^3}$.
$\Rightarrow {a^3} = {9^3} = 729{\text{ c}}{{\text{m}}^3}$
Hence, the volume of the cubical box is 729 ${\text{c}}{{\text{m}}^{\text{3}}}$.