The radius of a circle is increased so that circumference increases by 5%. By how much percentage will the area increase?
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≡QUESTION≡
The radius of a circle is increased so that circumference increases by 5%. By how much percentage will the area increase?
║⊕ANSWER⊕║
Area of circle, A = πr²
Radius of circle is increased by 5%
Increased radius = 105/100
= 1.05 unit
Increased area = π(105/100)² - 1π
= π(1.05)² - 1π
= 1.1025π
= (1.1025 - 1)π
= 0.1025π unit²
Percentage Increase = (0.1025/1) × 100
= 10.25%
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