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) plz send the answer on paper I really want

Answer 1

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


Hope it helps
:)

Answer 2

Given that 

Length = a 

Breadth = b 

Height = c 

Volume (v) = l x b x h

 = a x b x c = abc 

Surface area = 2(lb + bh + hl) 

= 2(ab + bc + ac)

Now,

2/5 ( 1/a +1/b + 1/c )

2/2(ab+bc+ac) (ab +bc + ca)/ abc

1/abc= 1/V

HENCE PROVED//