Question

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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/c]

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Answer 1

Volume V = a x b x c= abc

Surface area S= 2(ab+bc+ca)

Now,

LHS = 1/V= 1/abc

RHS = 2/S[1/a + 1/b +1/c]

= 2/2(ab+bc+ca) x (ab+bc+ca)/abc

= 1/abc

LHS=RHS(Hence proved)

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Answer 2

$\huge\mathfrak{Bonjour!!}$

$\huge\mathcal\purple{Solution:-}$

♨ Given:-

We have,

V→ Volume of the cuboid.

S→ Surface area of the cuboid.

a,b,c→ Dimensions of the cuboid.

♨ To prove:-

1/V = [2/S][1/a + 1/b + 1/c]

♨ Proof:-

We know that,

S= 2 (ab + bc + ca)

And

v= abc or

1/V = 1/abc

= S/S(abc)

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

[Since, S= 2 (ab + bc + ca)]

= [2/S] [ab/abc + bc/abc + ca/abc]

= [2/S] [ 1/c + 1/a + 1/b]

Therefore,

1/V = [2/S][1/a + 1/b + 1/c]

Hence proved!!☃

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