Question 116

If the radius of a circle is decreased by 10%, then what will be the percentage decrease in the area of circle?

Solution

Let radius of circle = $$r=10$$ cm

=> Area of circle = $$A=\pi r^2=\pi(10)^2=100\pi$$ $$cm^2$$

After decreasing the radius by 10%, => New radius = $$r'=10-(\frac{10}{100}\times10)=9$$ cm

=> New area of circle = $$A'=\pi(9)^2=81\pi$$ $$cm^2$$

$$\therefore$$ Decrease in area = $$\frac{(100-81)}{100}\times100=19\%$$

=> Ans - (A)

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