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Question

If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that: 1V=2S(1a+1b+1c).


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Solution

Given, the dimensions of cuboid are

l=a, b=b and h=c

Step 1: Find the volume V of the cuboid.

Volume of cuboid =lร—bร—h

V=aร—bร—c

V=abc-------(i)

Step 2: Find the surface area S of the cuboid.

Surface are of cuboid =2lb+bh+hl

S=2ab+bc+ca-------(ii)

Step 3: Divide equation (ii) by (i)

โ‡’SV=2ab+bc+caabc

โ‡’SV=2ababc+bcabc+caabc

โ‡’SV=21c+1a+1b

Divide both side by S, then we get

โˆด1V=2S1a+1b+1c

Hence proved.


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