If $V$ be the volume and $S$ the surface area of a cuboid of dimensions $a,b,$ and $c,$ then $\frac{1}{V}$ is equal to

The correct option is A: $\frac{2}{S}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$

Given: Dimensions of a cuboid are $a\times b\times c$

Volume of a cuboid $=length\times breadth\times height$

$\therefore V=abc\dots \dots \left(i\right)$

Surface Area of Cuboid $=2(length\times breadth+breadth\times height+length\times height)$

$S=2(ab+bc+ac)\dots \dot{(}ii)$

On dividing $eq.\left(ii\right)$ by $\left(i\right),$ we get

$\frac{S}{V}=\frac{2ab}{abc}+\frac{2bc}{abc}+\frac{2ac}{abc}$

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

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