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/c]`

Answer 1

The volume (V) of a cuboid = a x b x c

`:. 1/V = 1/(abc)` .......(1)

The surface area (S) of a cuboid = 2(ab + bc + ca)      .....(2)

`2/S = 1/(ab+bc+ac)`

RHS = `2/S (1/a +  1/b + 1/c)= 1/(ab +bc+ac)(1/a+1/b+1/c)`

`2/S xx (1/a+1/b+1/c) = 1/(abc)`

`:. 2/S xx(1/a+ 1/b + 1/c)= 1/V`