Question 112

The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm. Find the ratio of the areaof the annular zone to the area of the larger circle. (Area of the annular zone is the difference between the area of the larger circle and that of the smaller circle).

Solution

Area of circle = $$\pi r^2$$

Area of annular zone = $$\pi (5^2 - 3^2) = 16 \pi$$ sq. units

Area of larger circle = $$\pi * 5^2 = 25 \pi$$ sq. units

=> Required ratio = 16 : 25

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