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The lateral surface area of a cube is $324 \mathrm{~cm}^{2}$. Find its volume and the total surface area.

Solution

Let each side of the cube be $a \mathrm{~cm}$.

Then, the lateral surface area of the cube $=\left(4 a^{2}\right) \mathrm{cm}^{2}$.

$\therefore \quad 4 a^{2}=324 \Rightarrow a^{2}=81 \Rightarrow a=\sqrt{81}=9$.

Volume of the cube $=a^{3} \mathrm{~cm}^{3}$

=(9 × 9 × 9) cm³ =729 cm³

Total surface area of the cube $=\left(6 a^{2}\right)$ sq units

= (6 ×9 ×9) cm³ = 486 cm³

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