Question 135

The difference between the radii of the bigger circle and smaller circle is 14 cm and the difference between their areas is 1056 cm . Radius of the smaller circle is

Solution

Let the radius of bigger circle be $$R$$ and of smaller circle be $$r$$

=> $$R - r = 14$$ ----------Eqn(1)

Also, $$\pi R^2 - \pi r^2 = 1056$$

=> $$(R-r) (R+r) = \frac{1056}{\pi}$$

=> $$R + r = \frac{1056 * 7}{22 * 14}$$

=> $$R + r = 24$$ -----------Eqn(2)

Subtracting eqn(1) from (2), we get :

=> $$2r = 10$$

=> $$r = 5$$ cm

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