Question

if 'v' is volume of cuboid of dimensions a, b, c and 'S' is its surface area than prove that 1/v=2/S(1/a +1/b+1/c)

Answer 1

Hi ,

a , b , c are dimensions of the

cuboid.

S = 2 ( ab + bc + ca )

V = abc

RHS = 2/S(1/a + 1/b + 1/c )

= 2/[ 2( ab+bc+ca )] { 1/a+ 1/b + 1/c}

= 1/( ab+ bc +ca ) {( bc + ac + ab )/abc }

= 1/abc

= 1/V

= LHS

I hope this helps you.

:)