Circle – radius reduced by half: If the radius of a circle is decreased by 50%, what is the percentage decrease in its area?
Aptitude
Area
Difficulty: Easy
Choose an option
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A75%
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B65%
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C35%
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D25%
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ENone of these
Answer
Correct Answer: 75%
Explanation
Introduction / Context:Area of a circle depends on the square of the radius. A percentage change in radius does not translate linearly to area.
Given Data / Assumptions:
- Original radius = r.
- New radius = 0.5*r.
Concept / Approach:Area ∝ r^2. New area = (0.5)^2 times old area = 0.25 of original. Decrease = 75%.
Step-by-Step Solution:
Original area = πr^2.New area = π(0.5r)^2 = 0.25πr^2.Decrease = (1 − 0.25)*100% = 75%.Verification / Alternative check:Pick r = 10 → original area 100π; new radius 5 → new area 25π. Drop = 75π → 75%.
Why Other Options Are Wrong:65%, 35%, 25% are linear-style misreads; area scales quadratically, not linearly.
Common Pitfalls:Applying 50% directly to area instead of squaring the radius factor.
Final Answer:75%