Question

if volume of cuboid dimensions a
$a \times b \times c$
and S is surface area then prove
$\frac{1}{ v} = \frac{2}{s} ( \frac{1}{a } + \frac{1}{b} + \frac{1}{c} )$
​

Answer 1

Step-by-step explanation:

Dimensions of a cuboid:

Length = a units,

Breadth = b units,

Height = h units

Volume \: of \: the \: cuboid\\(V) = abc\:--(1)

Surface \: Area \\(S)=2(ab+bc+ca)\:---(2)

Now,\\RHS=\frac{2}{S}[\frac{1}{a}+\frac{1}{b}+\frac{1}{c}]

=\frac{2}{S}[\frac{bc+ac+ab}{abc}]

=\frac{2}{2(ab+bc+ca)}[\frac{(ab+bc+ca)}{abc}]

=\frac{1}{abc}

=\frac{1}{V}\\=LHS

Therefore,

\frac{2}{S}[\frac{1}{a}+\frac{1}{b}+\frac{1}{c}]=\frac{1}{V}

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