Q.1 The volume of a sphere of diameter 1 unit is ________ than the volume of a cube of side 1 unit.
(A) least (B) less (C) lesser (D) low
Correct Answer: (B) less
The volume of a sphere with diameter 1 unit is less than the volume of a cube with side 1 unit.
Volume Calculations
The volume of the cube is Vcube = 1³ = 1 cubic unit.
For the sphere, the radius r = 0.5 units, so its volume is:
Vsphere = 4/3π(0.5)³ = 4/3π(1/8) = π/6 ≈ 0.5236 cubic units.
Since π/6 < 1, the sphere’s volume is smaller.
Introduction to Volume Comparison
The volume of a sphere of diameter 1 unit compared to a cube of side 1 unit reveals key geometry principles. This question tests both math formulas and English precision, common in competitive exams. Understanding why one is less helps in quantitative aptitude.
Step-by-Step Calculation
- Cube volume: Side length 1 unit gives 1 × 1 × 1 = 1.
- Sphere radius: Diameter 1 unit means r = 0.5. Formula V = 4/3πr³ = π/6 ≈ 0.5236.
- Difference: Sphere occupies less space due to curved boundaries versus cube’s straight edges.
Why “Less” is Correct
- Least: Superlative for 3+ items; invalid here.
- Less: Standard for two quantities (0.5236 < 1).
- Lesser: Informal, rank-focused.
- Low: Non-comparative adjective.
This confirms volume of a sphere of diameter 1 unit is less.
