# If A1, A2, and A3 Denote the Areas of Three Adjacent Faces of a Cuboid, Then Its Volume is - Mathematics

MCQ

If A1, A2, and A3 denote the areas of three adjacent faces of a cuboid, then its volume is

#### Options

• A1 A2 A3

• 2A1 A2 A3

• $\sqrt{A_1 A_2 A_3}$

• ${}^3 \sqrt{A_1 A_2 A_3}$

#### Solution

We have;

Here A1A2 and A3 are the areas of three adjacent faces of a cuboid.

But the areas of three adjacent faces of a cuboid are lbbh and hl, where,

l →Length of the cuboid

b → Breadth of the cuboid

h → Height of the cuboid

We have to find the volume of the cuboid

Here,

A_1A_2A_3a = (lb)(bh)(hl)

= (lbh)(lbh)

=(lbh)^2

=V^2                             {"Since ,V = lbh"}

V = sqrt(A_1A_2A_3)

Thus, volume of the cuboid is  sqrt(A_1A_2A_3).

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 17 | Page 36

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