Question

The volume of a cuboid with sides a, b and c is v and its surface area is s then ………………… 

A) V = 2 s (a + b + 1) 

B) V = 2 (\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\) ) 

C) (b + c) 

D) \(\frac{1}{V} = \frac{2}{s}\) (\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\))

Answer 1

Correct option is (D) \(\frac{1}{V}=\frac{2}{s}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\)

Volume of cuboid is V = abc   ________(1)

Surface area of cuboid is S = 2 (ab+bc+ca)    ________(2)

Dividing equation (2) by (1), we get

\(\frac{S}{V}=\frac{2(ab+bc+ca)}{abc}\)

\(\Rightarrow\) \(\frac{S}{V}=2(\frac1c+\frac1a+\frac1b)\)

\(\Rightarrow\) \(\frac{1}{V}=\frac{2}{s}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})\)

\(\therefore\) Correct option is (D)

Answer 2

D) \(\frac{1}{V} = \frac{2}{s}\) (\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\))