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If V is the Volume of a Cuboid of Dimensions A, B, C and S is Its Surface Area, Then Prove that `1/V=2/S(1/A+1/B+1)` - Mathematics

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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

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

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Solution

Given that
Length = a
Breadth = b
Height = c

Volume `(v)=lxxbxxh`
`=axxbxxc=abc`

Surface area `2(lb+bh+hl)`

`=2(ab+bc+ac)`

`Now , 2/5[1/a+1/b+1/c]=2/(2(ab+bc+ca)) [[ab+bc+ca]]/(abc)`

`1/(abc)=1/v`

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Chapter 18: Surface Areas and Volume of a Cuboid and Cube - Exercise 18.2 [Page 31]

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RD Sharma Mathematics [English] Class 9
Chapter 18 Surface Areas and Volume of a Cuboid and Cube
Exercise 18.2 | Q 20 | Page 31

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