If the areas of three consecutive faces of a cuboid are 12 cm2, 20 cm2

1.	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 is1. 120 cm32. 60 cm33. 150 cm34. 180 cm3
Answer» 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.

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 is1. 120 cm32. 60 cm33. 150 cm34. 180 cm3

Answer» 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.

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