If V is the volume of 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)

Question

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

\(\cfrac{1}{V}=\cfrac2S\Big(\cfrac{1}a+\cfrac{1}b+\cfrac{1}c\Big)\)

Answer 1

Given, V= volume of cuboid

S = surface area of cuboid

=a = length of cuboid

=b =breadth of cuboid

= c = height of cuboid

V = abc

S = 2(ab + bc + ca)

Dividing surface area by volume

Proved