Question

Help!
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RD Sharma IXth
[Surface Area and Volumes.]

Dekhna 2nd Level ka h -,- ​

Answer 1

Answer:

Given:-

a, b and c are dimensions of the cuboid.

a - length

b - breadth

c - height

S is its surface area and V is the volume of the cuboid.

To prove:-

$\frac{1}{v} = \frac{2}{s} ( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} )$

Solution:-

We know that,

Volume of a cuboid = a × b × c

And Surface area = 2(lb + bh + hl)

= 2(ab + bc + ca)

Let R.H.S

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

And L.H.S

$= \frac{1}{v}$

$\Longrightarrow \: \frac{1}{v} = \frac{2}{s} ( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} ) \\ \\\Longrightarrow \: \frac{1}{v} = \frac{2}{2(ab + bc + ac)} ( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} ) \\ \\ \Longrightarrow \: \frac{1}{v} = \frac{1}{ab + bc + ac} ( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} ) \\ \\ \: \\ = \frac{1}{ab + bc + ac} ( \frac{ab + bc + ac}{abc} ) \\ \\ = \frac{1}{abc}$

$\Longrightarrow \: \frac{1}{v} = \frac{1}{abc} \\ \\\Longrightarrow \: \frac{1}{abc} = \frac{1}{abc} \: \: \: \: (since \: v \: = abc)$

Hence, proved.

Answer 2

V denotes volume

S denotes surface area

a,b,c denotes dimensions