Question

If l, b, h, S, and V are length, breadth, height, surface area, and volume respectively of a cuboid, then which of the following options are correct?

• A.
• B.
• C.
• D.

Answer 1

Answer: (A), (D)

The correct options are
A
D

Surface area of a cuboid, $S=2(lb+bh+lh)$

Volume of cuboid, $v=lbh$

On Dividing surface area by volume, we get

$\frac{s}{v}=\frac{2(lb+bh+lh)}{lbh}$

$\Rightarrow \frac{s}{v}=2[\frac{lb}{lbh}+\frac{bh}{lbh}+\frac{lh}{lbh}]$

$\Rightarrow \frac{s}{v}=2[\frac{1}{h}+\frac{1}{l}+\frac{1}{b}]$

$\Rightarrow \frac{s}{v}=2[\frac{1}{l}+\frac{1}{b}+\frac{1}{h}]$

$\Rightarrow \frac{1}{v}=\frac{2}{s}[\frac{1}{l}+\frac{1}{b}+\frac{1}{h}]$

Hence, the correct option is D.