Circle comparison: For a circle of radius 5 units, the area is numerically what percent of its circumference?

Difficulty: Easy

Correct Answer: 250%

Explanation:


Introduction / Context:
Relates two basic measures of a circle: area and circumference, then converts their ratio to a percentage for a given radius.


Given Data / Assumptions:

  • r = 5 (units)
  • Area A = πr^2
  • Circumference C = 2πr


Concept / Approach:
Compute A and C, then find (A/C)*100 percent. Note that π cancels out.


Step-by-Step Solution:

A = π * 5^2 = 25πC = 2π * 5 = 10πPercentage = (A / C) * 100 = (25π / 10π) * 100 = 2.5 * 100 = 250%


Verification / Alternative check:
Since A/C = r/2, for r = 5 we get 2.5 → 250%.


Why Other Options Are Wrong:
150%, 350%, 450%, 200% do not match the exact ratio r/2 for r = 5.


Common Pitfalls:
Forgetting to cancel π or squaring the wrong quantity when computing area vs circumference.


Final Answer:
250%

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