Multiple choice

A piece of wire of length 33 cm is bent into an arc of a circle of radius 14 cm. What is the angle subtended by the arc at the centre of the circle?

  1. 75°

  2. 90°

  3. 135°

  4. 150°
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C Correct answer
Explanation

Arc length L = 33, radius r = 14. L = r * theta (in radians). 33 = 14 * theta. theta = 33/14 radians. Convert to degrees: (33/14) * (180/pi) = (33/14) * (180 / (22/7)) = (33/14) * (180 * 7 / 22) = (3/2) * 90 = 135 degrees.

AI explanation

The formula relating arc length, radius, and the central angle in degrees is Angle = (Arc Length * 180) / (pi * radius). Substituting the given values gives Angle = (33 * 180) / ((22/7) * 14). This simplifies to Angle = 5940 / 44, which equals 135 degrees. The angle subtended by the arc at the center is 135 degrees.

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