Question 6

If the radius of a circle is decreased to 25% of its original value, calculate the percentage decrease in the area of the circle.

Solution

Let the radius of the circle initially = $$r=20$$ cm

=> Area = $$A=\pi r^2=\pi(20)^2=400\pi$$

New radius = $$r'=20-(\frac{25}{100}\times20)=15$$ cm

=> New Area = $$A'=\pi(15)^2=225\pi$$

$$\therefore$$ Percent decrease in area = $$\frac{(400\pi-225\pi)}{400\pi}\times100$$

= $$\frac{175}{4}=43.75\%$$

=> Ans - (B)

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