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in Areas Related To Circles by (23.7k points)
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The radius of a circle is so increased, that its circumference is increased by 5%. The area of the circle, then increases by

(a) 12.5% 

(b) 10.25% 

(c) 10.5% 

(d) 11.25%

1 Answer

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Answer : (b) 10.25% 

Let r be the radius of the circle. Then,

Increased circumference = 2πr + 2πr × \(\frac{5}{100}\) = \(\frac{21\pi r}{10}\)

∴ If R be the radius of the increased circle, then 

2πR = \(\frac{21\pi r}{10}\) ⇒ R = \(\frac{21 r}{20}\)

∴  Radius of increased circle = \(\frac{21 r}{20}\) 

∴ Percentage increase in area = \(\frac{\frac{41\pi r^2}{400}}{\pi r^2}\)  × 100 % 

= 10.25 %

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