Question

Heyyaa!❣
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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].​

Answer 1

Dimensions of cuboid are,

length (l) = a

breadth (b) = b

height (h) = c

volume of cuboid = length × breadth × height

=> V = a×b×c

surface area of cuboid = 2 ( lb + bh + hl )

=> 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) × [ bc + ac + ab ] / (abc)

=> 1/(ab + bc + ca) × (bc + ac + ab)/ abc

=> 1/(abc)

=> 1/V = LHS

Proved.