Question

If V is the volume of cuboid, S is the total surface area and a, b, c are its edges, then prove that 1/V = 2/S(1/a +1/b +1/c).
Plz answer at the earliest!

Answer 1

Given dimensions of cuboid are a, b and c. Therefore, volume of cuboid, V = abc  → (1) Surface area of cuboid, S = 2(ab + bc + ca)  → (2) Now divide (2) with (1), we get 

Answer 2

Given dimensions of cuboid are a,b and c. Therefore, volume of cuboid,

V=abc (equation 1)

Surface area of cuboid,

S= (ab+bc+can) ( equation 2)

S/V = 2(ab+bc+can)/ABC

= 2[(ab/abc)+(bc/abc)+(ca/abc)]

= 2[1/c + 1/a + 1/b]

Hence 1/v=2/s [1/c + 1/a + 1/b]