Question

If v is the volume of a cuboid of dimension l,b,h and s is surface area then prove 1/v = 2/s (1/l + 1/b + 1/h ).​

Answer 1

Step-by-step explanation:

We know that

Volume of a cuboid = a × b × c

Surface area of cuboid = 2 (ab + bc + ac)

So we get

2/s (1/a + 1/b + 1/c) = 2/s ((bc + ac + ab)/abc)

It can be written as

2/s (1/a + 1/b + 1/c) = 2/s (s/2V)

On further calculation

2/s (1/a + 1/b + 1/c) = 1/V

We get

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

Therefore, it is proved that 1/V = 2/S (1/a + 1/b + 1/c).