The areas of three adjacent faces of a solid cuboid are 66 cm², 108 cm² and 198 cm². what is the volume (in cm³) of the cuboid?

Correct option is B

Given:

The areas of three adjacent faces of a cuboid are:

​$$A_1 = 66 \, \text{cm}^2$$​​

​$$A_2 = 108 \, \text{cm}^2$$​​

​$$A_3 = 198 \, \text{cm}^2$$​​

Formula Used:

Volume of cuboid,V = $$\sqrt{(ab)(bc)(ca)}$$​​

Where a, b, c are dimensions

Solution:

Let the dimensions of the cuboid be a, b, and c. So, the areas of the three faces are:

​$$A_1 = ab = 66 \, \text{cm}^2$$​​

​$$A_2 = bc = 108 \, \text{cm}^2$$​​

​$$A_3 = ca = 198 \, \text{cm}^2$$​​

Now,

​$$V^2 = (66)(108)(198)$$​​

​$$V^2 = 1411334$$​​

V = $$\sqrt{1411334} = 1188 \, \text{cm}^3$$​​

The volume of the cuboid is 1188 cm³.