Multiple choice

The area of the ring between two concentric circles, whose circumference are $88cm$ and $132cm$, is:

  1. $780{cm}^{2}$
  2. $770{cm}^{2}$
  3. $715{cm}^{2}$
  4. $660{cm}^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Circumference C = 2*pi*r. For C=88, r1 = 88/(2*pi) = 14. For C=132, r2 = 132/(2*pi) = 21. Area of ring = pi*(r2^2 - r1^2) = pi*(441 - 196) = pi*245. Using pi = 22/7, Area = (22/7)*245 = 22*35 = 770.

AI explanation

Using the circumference formula 2 * pi * r, the radii of the two circles are 88 / (2 * (22/7)) = 14 cm and 132 / (2 * (22/7)) = 21 cm. The area of the ring is the difference between the areas of the two circles, pi * (R squared - r squared). Substituting the values gives (22/7) * (21 squared - 14 squared) = (22/7) * (441 - 196) = 770 sq. cm.

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