Question

If V be the volume of the cuboid of dimensions a, b and c and S its total surface area then $\frac{4}{S}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$ in terms of V is equal to

• A. $\frac{8}{V}$
• B. $\frac{2}{V}$
• C. $\frac{4}{V}$
• D. $\frac{1}{V}$

Answer 1

The correct option is B $\frac{2}{V}$

Volume of cuboid=abc

Surface area if cuboid, $S=2(ab+bc+ca)$

Now, $\frac{S}{V}=\frac{2(ab+bc+ca)}{abc}=2[\frac{1}{c}+\frac{1}{a}+\frac{1}{b}]$

$\Rightarrow \frac{S}{V}=2[\frac{1}{a}+\frac{1}{b}+\frac{1}{c}]\Rightarrow \frac{2S}{V}=4(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$

$\Rightarrow \frac{2}{V}=\frac{4}{S}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$