Question

If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then `A/V`

Options

•  x²y²z²

• \[\frac{1}{2}\left( \frac{1}{xy} + \frac{1}{yz} + \frac{1}{zx} \right)\]

   

• \[\left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right)\]

   

• \[\frac{1}{xyz}\]

   

Answer 1

Dimensions of the cuboid are x,y,z.

So, the surface area of the cuboid (A) = 2 (xy + yz + zx)

Volume of the cuboid (V) = xyz 

`A/V = (2(xy + yz + zx))/(xyz)`

    `=2((xy)/(xyz) + (yz)/(xyz)+(zx)/(xyz))`

   `=2(1/x +1/y+1/z)`