Question

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

• A. $x^2{y}^2{z}^2$
• B. $\frac{1}{2}(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx})$
• C. $2(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})$
• D. $\frac{1}{xyz}$

Answer 1

The correct option is C

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

A is surface area, V is volume and x, y and z are the dimensions

Then V = xyz

$A=2[xy+yz+zx]$

$\frac{A}{V}=\frac{2[xy+yz+zx]}{xyz}$

$=2[\frac{xy}{xyz}+\frac{yz}{xyz}+\frac{zx}{xyz}]$

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