Question

Dimensions of a cube is a, b and c. Find the relation between surface area and volume.

Answer 1

Given dimensions of cuboid are a, b and c. Therefore, volume of cuboid, $V=abc\to \left(1\right)$
Surface area of cuboid, $S=2(ab+bc+ca)\to \left(2\right)$
Now divide (2) with (1), we get
$\frac{S}{V}=\frac{2(ab+bc+ca)}{abc}$
$=2[\frac{ab}{abc}+\frac{bc}{abc}+\frac{ca}{abc}]$
$=2[\frac{1}{c}+\frac{1}{a}+\frac{1}{b}]$
Hence $\frac{1}{v}=\frac{2}{s}[\frac{1}{c}+\frac{1}{a}+\frac{1}{b}]$