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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.., $6{a^2} = 486$ 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 ${a^3}$.

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.

Given,

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 ${a^3}$.

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.