If V is the Volume of a Cuboid of Dimensions X, Y, Z and a is Its Surface Area, Then a V - Mathematics

MCQ

If V is the volume of a cuboid of dimensions xyz and A is its surface area, then A/V

Options

•  x2y2z2

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

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

• $\frac{1}{xyz}$

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)

Concept: Surface Area of a Cuboid
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 18 Surface Areas and Volume of a Cuboid and Cube
Exercise 18.4 | Q 19 | Page 36

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