Multiple choice

If the radius of a circle is increased by 50%, then the area of the circle is increased by:

  1. $125%$
  2. $100%$
  3. $75%$
  4. $50%$
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A Correct answer
Explanation

Original radius = r, area = πr². New radius = 1.5r (50% increase). New area = π(1.5r)² = 2.25πr². Increase = 2.25πr² - πr² = 1.25πr². Percentage increase = (1.25πr² / πr²) × 100 = 125%. The area scales with the square of the linear dimension.

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