Q16 (c) (ii)

Criteria	Marks
Provides correct solution	2
Applies part (i) to $ab$, $ac$ and $bc$, or equivalent merit	1

Sample answer:
Given a cube, we have $a=b=c$.
$V=abc=a^3$
$S=2(ab+ac+bc)=6a^2$

$$\left(\frac S6\right)^{3/2}=\left(\frac{6a^2}{6}\right)^{3/2}=a^3$$

$V=\left(\frac S6\right)^{3/2}$
From part (i) we know that $V\le\left(\frac S6\right)^{3/2}$ for all rectangular prisms.
Hence a cube has maximum possible volume for a fixed surface area.