Question 68

If the radius of a circle is decreased by 30%, then what is the decrease in the area of the circle?

Solution

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

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

If the radius of a circle is decreased by 30%, new radius = $$r'=10-(\frac{30}{100}\times10)$$

= $$10-3=7$$ cm

=> New area = $$A'=\pi(7)^2=49\pi$$ $$cm^2$$

$$\therefore$$ Decrease in area of circle = $$\frac{(100\pi-49\pi)}{100\pi}\times100$$

= $$51\%$$

=> Ans - (A)


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