Question 16

If C1 and C2 are the circumferences of the outer and inner circles respectively. What is C1 : C2?
(I) The two circles are concentric.
(II) The area of the ring is $$\frac{2}{3}$$ the area of greater circle.

Solution

The area between the 2 circles is $$\pi\ $$(R^2 - r^2). The ratio of this area to that of the bigger circle's is 2/3.

So, $$\pi\ $$(R^2 - r^2) = (2/3) $$\pi\ $$(R^2)

=> (R^2) = 3 x (r^2)

=> r/R = (1/$$\sqrt{\ 3}$$)

=> (2$$\pi\ $$r)/(2$$\pi\ $$R) = (1/$$\sqrt{\ 3}$$) = C1:C2

$$\therefore\ $$ Statement II alone is sufficient to answer the question.

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