Multiple choice

Consider a circle of diameter 60 m with a chord of length 30 m. Compute the length of the minor arc on one side of the chord and the length of the major arc.

  1. 31.42 and 151.1

  2. 31.42 and 157.1

  3. 31.11 and 151.7

  4. 31.11 and 151.1

  5. 30.21 and 149.36
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Radius r = 30. Chord length = 30. This forms an equilateral triangle with the center, so the central angle is 60 degrees (pi/3 radians). Minor arc = r * theta = 30 * (pi/3) = 10 * pi = 31.4159. Major arc = 2 * pi * r - 31.4159 = 188.495 - 31.4159 = 157.08.

AI explanation

The radius is 30 m and the chord is 30 m, forming an equilateral triangle with the center that yields a central angle of 60 degrees or pi/3 radians. The minor arc is calculated as r * theta = 30 * (pi/3) = 10pi, which is approximately 31.42 m. The major arc corresponds to the remaining angle of 300 degrees or 5pi/3 radians, so its length is 30 * (5pi/3) = 50pi, which is approximately 157.1 m. This matches the lengths 31.42 and 157.1.

Keep practicing — related questions