Circle Formulae
1. Area: $$\pi\ r^2$$
2. Circumference: $$2\pi r$$
3. Length of Arc: $$\left(\frac{\theta}{360}\right)\left(2\pi r\right)$$
4. Area of Sector: $$\left(\frac{\theta}{360}\right)\left(\pi r^2\right)$$
Circle - Formulae
Rarely Tested
Question 1
Three concentric circles A, B and C have radii in the ratio 1:2:4. What is the ratio of area enclosed between A and B and the area enclosed between B and C
Solution
Area enclosed between A and B(region 1) = area of circle B - area of circle A = $$\pi\ \left(2\right)^2-\pi\ \left(1\right)^2=3\pi\ $$
Area enclosed between B and C(region 2) = area of circle C - area of circle B = $$\pi\ \left(4\right)^2-\pi\ \left(2\right)^2=12\pi\ $$
Required ratio = $$\frac{3\pi}{12\pi\ }=\frac{1}{4}\ $$
The answer is option C.
Question 2
The sum of the areas of two circles touching each other externally is 170$$\pi$$ sq cm and the distance between the centres of the two circles is 18 cm. Find the ratio of the radii of the two circles?
Solution
$$x^{2}$$ + $$y^{2}$$ = 170 and x + y = 18. So, x = 11 cm and y = 7 cm
Question 3
The sum of the areas of two circles touching each other internally is 233$$\pi$$ sq cm and the distance between the centers of the two circles is 5 cm. Find the ratio of the radii of the two circles?
Solution
$$x^{2}$$ + $$y^{2}$$ = 233 and x - y = 5. So, x = 13 cm and y = 8 cm
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Previous Year Stats
Circle - Formulae
2
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