The total surface area of a cube is $216 \mathrm{~cm}^{2}$. Find its volume.
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The total surface area of a cube is $216 \mathrm{~cm}^{2}$. Find its volume.
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 Solution

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

Then, the total surface area of the cube $=\left(6 a^{2}\right) \mathrm{cm}^{2}$.

$\therefore \quad 6 a^{2}=216 \Rightarrow a^{2}=36 \Rightarrow a=\sqrt{36}=6$.

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

= (6×6×6) cm3 = 216 cm³.

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