If $v$ is the volume of a cuboid of dimensions $x, y, z$ and $A$ is its surface area, then $\frac{A}{V}$ is?

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Solution

Given:
Dimensions of cuboid $= x, y$ and $z$

$∴$ Volume of cuboid $(V) = x y z$

Surface area of cuboid $(A) = 2 (x y + y z + z x)$

$\frac{A}{V} = \frac{2 (x y + y z + z x)}{x y z}$

$= 2 (\frac{1}{z} + \frac{1}{x} + \frac{1}{y})$

$= 2 (\frac{1}{x} + \frac{1}{y} + \frac{1}{z})$

Hence, (c) is the correct option.

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