Question
CBSEENMA9003495

If v is the volume of a cuboid of dimensions a, b and c and s is its surface area, then prove that

             1 over straight v equals 2 over straight s open parentheses 1 over straight b plus 1 over straight b plus 1 over straight c close parentheses

Solution

L. H. S. = 1 over straight v equals negative 1 over abc space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis
R. H. S. = 2 over straight s open parentheses 1 over straight a plus 1 over straight b plus 1 over straight c close parentheses
       equals fraction numerator 2 over denominator 2 left parenthesis ab plus bc plus ca right parenthesis end fraction open parentheses fraction numerator bc plus ca plus ab over denominator abc end fraction close parentheses
equals space 1 over abc space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis
(1) and(2) given
1 over straight v equals 2 over straight s open parentheses 1 over straight a plus 1 over straight b plus 1 over straight c close parentheses

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