Question

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

• \[\sqrt{A_1 A_2 A_3}\]

   

• \[{}^3 \sqrt{A_1 A_2 A_3}\]

   

Answer 1

We have;

Here A₁, A₂ and A₃ are the areas of three adjacent faces of a cuboid.

But the areas of three adjacent faces of a cuboid are lb, bh 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)`.