Question

use formula of volume of cuboid
and its surface area

Answer 1

$\text{Let the length, breadth and height of the cuboid be a, b and c respectively.}$

$\text{Then,} \\ \text{ Volume of cuboid = abc} \: \: (1) \\ \text{Surface area of cuboid = 2(ab+bc+ac)} \: \: (2)$

$\text{Divide (2) by (1)} \\ \frac{\text{Surface area of cuboid}}{\text{Volume of Cuboid}} = \frac{\text{2(ab+bc+ac)}}{\text{abc}} \\ \\ \frac{S}{V} = 2 \bigg(\frac{1}{a} + \frac{1}{b}+\frac{1}{c} \bigg) \\ \\ \boxed{\frac{1}{V} = \frac{2}{S} \bigg(\frac{1}{a} + \frac{1}{b}+\frac{1}{c} \bigg)}$