Question

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

\({\frac{1}{V} = \frac{2}{S}} \)\(({1 \over a} + {1 \over b} + {1\over c})\)

Answer 1

Dimensions of a cube are: 

Length = l = a 

Breadth = b = b 

Height = h = c 

We know, 

Volume of the cube (V) = lbh 

= a x b x c 

Or V = abc ….(1) 

Again, Surface area of the cube (S) 

= 2 (lb+bh+hl) 

or S = 2 (ab+bc+ca) ……(2)

Now,