Question

Prove that: 1/v = 2/s (1/a +1/b +1/c ) where, v=volume of cuboid, s= surface area of the cuboid , a,b and c are length, breadth and height of the cuboid respectively.

Answer 1

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Answer 2

As volume of cuboid = l×b×h

=a×b×c=abc

And total surface area = 2(lb+bh+hl)

=2(ab+bc+ca)

NOW,

V= abc & S=2(ab+bc+ca)

So we can write S/2=ab+bc+ca

If we reciprocal second  equation then it will be

2/S=(1/ab+1/bc+1ca)

NOW,WE WILL SOLVE ABOVE EQUATION:

2/S=(a+b+c/abc) as we have taken L.C.M. of ab+bc+ca which is equal to abc

NOW PUT THE VALUE OF abc

We will get

2/S=(a+b+c/V)

NOW CROSS MULTIPY IT :

2V=S(a+b+c)

And then

V=S/2(a+b+c)

Again reciprocal it

We will get

1/V=2/S(1/a+1/b+1/c)

Hence proved