Circle comparison: For a circle of radius 5 units, the area is numerically what percent of its circumference?
Aptitude
Area
Difficulty: Easy
Choose an option
-
A150%
-
B250%
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C350%
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D450%
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E200%
Answer
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%