Question

If the areas of three consecutive faces of a cuboid are 12 cm², 20 cm², and 60 cm², then the volume (in cm³) of the cuboid is
1.  120 cm3
2.  60 cm3
3.  150 cm3
4.  180 cm3

Answer 1

Correct Answer - Option 1 :  120 cm3

Given:

The areas of three consecutive faces of a cuboid are 12 cm2, 20 cm2, and 60 cm².

Formula used:

The volume of cuboid = l × b × h

Where l → length

b → breadth

h → height

Calculations:

Let the length, breadth, and height of the cuboid be x, y, and z respectively.

Then xy = 12 cm2, yz = 20 cm², and zx = 60 cm² 

By multiplying these three we'll get

xy × yz × zx = 12 × 20 × 60

⇒ x²y²z² = 14400

⇒ (xyz)² = 14400

⇒ xyz = 120 and –120, (Rejecting the negative term as volume cannot be negative)

Volume of cuboid = l × b × h = xyz

Thus xyz = 120 cm³

∴ The volume of the cuboid is 120 cm³.