Question

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

Answer 1

Given that, the total surface area of a cubical box is $486c{m}^2$

To find out: Volume of the box.

Let $a$ be the side of the cubical box.

We know that the total surface area of a cuboid is $6a^2$

$\therefore 6a^2=486$

$\Rightarrow a^2=\frac{486}{6}$

$\Rightarrow a^2=81$

$\therefore a=9cm$

We also know that, the volume of a cuboid is $a^3$

$\therefore$ Volume of the box $=9^3$

$\Rightarrow 729c{m}^3$

Hence, the volume of the given cuboidal box is $729c{m}^3$.