A cuboid has areas of three mutually adjacent faces equal to 120 cm^2, 72 cm^2, and 60 cm^2. Find the volume of the cuboid.

Introduction / Context:If ab, bc, and ca (areas of three adjacent faces) are known for a cuboid with edges a, b, c, then the volume abc can be found without individually solving for a, b, c using the identity abc = √[(ab)(bc)(ca)]. This is a standard shortcut in 3D mensuration.

Given Data / Assumptions:

• ab = 120 cm^2, bc = 72 cm^2, ca = 60 cm^2.
• Volume V = abc.

Concept / Approach:Multiply the three face areas and take the square root: (ab)(bc)(ca) = (abc)^2. Then V = √(product). This avoids solving three equations for the three unknowns.

Step-by-Step Solution:(ab)(bc)(ca) = 120 * 72 * 60120 * 60 = 7200; 7200 * 72 = 518400V = √518400 = 720 cm^3

Verification / Alternative check:Optional factorization: 518400 = (720)^2 confirms the square root cleanly.

Why Other Options Are Wrong:820, 750 are arbitrary nearby integers; only 720 is the exact square root of the computed product.

Common Pitfalls:Forgetting that the product equals (abc)^2; arithmetic errors when multiplying three numbers; unit confusion.

Final Answer:720 cm3