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

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)

Solution:

Given Data:

Length of the cube (l) = a

Breadth of the cube (b) = b

Height of the cube (h) = c

Volume of the cube (V) = l * b * h

= a * b * c

= abc

Surface area of the cube (S) = 2 (lb + bh + hl)

= 2(ab + bc + ca)

Now, $\frac{\mathrm{ab}+\mathrm{bc}+\mathrm{ca}}{\mathrm{abc}} \frac{2}{2(\mathrm{ab}+\mathrm{bc}+\mathrm{ca})}=\frac{2}{\mathrm{~S}}\left(\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{~b}}+\frac{1}{\mathrm{c}}\right)$

Therefore, $\frac{1}{\mathrm{abc}}=\frac{2}{\mathrm{~S}}\left(\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{~b}}+\frac{1}{\mathrm{c}}\right)$

Therefore,$\frac{1}{V}=\frac{2}{S}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$

Hence Proved.