2019 · Q41
The areas of three adjacent faces of a cuboid are x, y and z. If V is the volume of the cuboid, then which one of the following is correct?
Elementary MathematicsMensuration
- AV = xyz
- BV² = xyz
- CV³ = xyz
- DV = (xyz)²
Explanation
Let the cuboid have edges l, b, h. Its three adjacent face areas are x = lb, y = bh and z = hl. Multiplying all three gives xyz = (lb)(bh)(hl) = (lbh)^2. Since the volume is V = lbh, we have (lbh)^2 = V^2, so xyz = V^2. Option A (V = xyz) wrongly equates volume with a product of areas (dimension mismatch: length^3 vs length^6), C inverts the relation, and D squares the wrong side. Hence V^2 = xyz, option B.