Question

If V is the volume of a cuboid of dimensions a × b × c and A is its surface area, then $\frac{A}{V}$ is

• A. $a^2{b}^2{c}^2$
• B. $2(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$
• C. $\frac{1}{abc}$
• D. $\frac{1}{2}(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca})$

Answer 1

The correct option is B $2(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$

We know, surface area of a cuboid of dimensions l×b×h, A = 2(lb + bh + hl)
So, surface area of a cuboid of dimensions a×b×c = 2(ab + bc + ca)
And, volume of the cuboid, V = abc
$\therefore \frac{\text{A}}{\text{V}}=\frac{2(ab+bc+ca)}{abc}=2(\frac{1}{c}+\frac{1}{a}+\frac{1}{b})$