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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
- \[\frac{1}{2}\left( \frac{1}{xy} + \frac{1}{yz} + \frac{1}{zx} \right)\]
- \[\left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right)\]
- \[\frac{1}{xyz}\]
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Solution
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)`
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