If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then A/V. A. x^2 y^2 z^2 B. 1/2(1/xy + 1/yz + 1/zx)

Question

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

A. x² y² z²

B. \(\cfrac{1}{2}\Big(\cfrac{1}{\text xy}+\cfrac{1}{yz}+\cfrac{1}{z\text x}\Big)\)

C. \(2\Big(\cfrac{1}{\text x}+\cfrac{1}{y}+\cfrac{1}{z}\Big)\)

D. \(\cfrac{1}{\text xyz}\) 

Answer 1

Correct option is C. \(2\Big(\cfrac{1}{\text x}+\cfrac{1}{y}+\cfrac{1}{z}\Big)\) 

Volume of a Cuboid = Length × Breadth × Height

Hence, Volume of a Cuboid V = xyz

Surface Area of a Cuboid = 2 × (Length × Breadth + Breadth × Height + Length × Height)

∴ Surface Area of a Cuboid A = 2 × (xy + yz + zx)