Multiple choice

A circle of radius 9 cm has an arc of length 12.1 cm. What is the angle subtended by the arc at the centre of the circle?

  1. 154°

  2. 231°

  3. 77°

  4. 38.5°
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C Correct answer
Explanation

Arc length s = r * theta (in radians). 12.1 = 9 * theta => theta = 12.1 / 9 radians. Convert to degrees: (12.1 / 9) * (180 / pi) = (12.1 * 20) / 3.14159 = 242 / 3.14159 = 77.03 degrees.

AI explanation

The formula relating arc length (l), radius (r) and the central angle (theta in degrees) is l equals 2 times pi times r times theta divided by 360. Substituting the given values, we get 12.1 equals 2 times 22 over 7 times 9 times theta divided by 360. Simplifying this gives theta equals 12.1 times 7 times 360 divided by 44 times 9, which results in an angle of 77 degrees.

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