The total surface area of a cube is $216 c m^{2}$ . Find its volume.

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Solution

$6 (E d g e)^{2} =$ Total surface area of a cube.
$∴ 6 (E d g e)^{2} = 216 c m^{2} \Rightarrow (E d g e)^{2} = \frac{216}{6} \Rightarrow (E d g e)^{2} = 36 \Rightarrow E d g e = \sqrt{36} \Rightarrow E d g e = 6 c m$
Volume of the given cube $= (E d g e)^{3}$
$= (6)^{3} = 6 \times 6 \times 6 = 216 c m^{3}$

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