Multiple choice

The length of minor arc $\widehat {AB}$ of a circle with radius $7$ units is $14$. Find the length of major arc $\widehat {AB}$.

  1. $18$
  2. $21$
  3. $28$
  4. $30$
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D Correct answer
Explanation

Circumference = 2 * pi * r = 2 * pi * 7 = 14 * pi. Minor arc = 14. Major arc = Circumference - Minor arc = 14*pi - 14 = 14(pi - 1). Using pi approx 3.14, 14 * 2.14 = 29.96, which is approx 30.

AI explanation

The radius of the circle is 7, so the total circumference is 2 times pi times 7, which equals 14 times pi. Using the approximation of pi as 22 divided by 7, the total circumference is 44 units. The length of the major arc is the total circumference minus the length of the minor arc, which is 44 minus 14. The length of the major arc is 30 units.

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