For a sphere with radius 10 cm, the numerical value of surface area is what percent of the numerical value of its volume?

Introduction / Context:
This question compares the numerical values of a sphere’s surface area and volume for a given radius. Although area and volume have different units, aptitude problems often request the percentage ratio of their numerical magnitudes for a fixed measurement.

Given Data / Assumptions:
Radius r = 10 cm. Surface area S = 4πr^2. Volume V = (4/3)πr^3.

Concept / Approach:
Compute S/V * 100%. The π factors cancel. The power of r reduces to 1 in the denominator, leaving a simple arithmetic fraction multiplied by 100. Substitute r = 10 to obtain a clean percentage.

Step-by-Step Solution:

Verification / Alternative check:
Approximate numerically: S ≈ 1256.6; V ≈ 4188.8; S/V ≈ 0.3 ⇒ 30%.

Why Other Options Are Wrong:
Values like 24%, 26.5%, or 45% do not match the exact ratio. 33.3% is a common distractor (one-third) but incorrect here.

Common Pitfalls:
Forgetting the factor 1/3 in volume, or failing to cancel π. Misplacing powers of r can also lead to wrong ratios.

Final Answer:
30%