Multiple choice

The radius of circle is $20$ cm The radii (in centimeters) of three concentric circle drawn in such a manner that the whole area is divided into four equal parts ,are

  1. $\displaystyle 20\sqrt{2},20\sqrt{3},10$
  2. $\displaystyle \frac{10\sqrt{3}}{3},\frac{10\sqrt{2}}{3},\frac{10}{3}$
  3. $\displaystyle 10\sqrt{3},10\sqrt{2},10$
  4. $17,14,10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The total area is pi*R^2 = pi*20^2 = 400*pi. Dividing into 4 equal parts means each ring/circle has area 100*pi. The radii r1, r2, r3 satisfy pi*r3^2 = 100*pi (r3=10), pi*r2^2 = 200*pi (r2=10*sqrt(2)), and pi*r1^2 = 300*pi (r1=10*sqrt(3)).

AI explanation

To divide the total area of the circle into four equal parts, the area up to the nth part from the center must equal n/4 of the total area. This gives pi * r_n^2 = (n/4) * pi * 20^2, meaning r_n = 20 * sqrt(n/4) = 10 * sqrt(n). Therefore, the radii for the first, second, and third concentric circles are 10, 10*sqrt(2), and 10*sqrt(3) cm respectively.

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