Multiple choice

An arc of length 44 cm makes an angle of 84° at the centre of a circle. The radius of the circle is _______.

  1. 30 cm

  2. 15 cm

  3. 20 cm

  4. 60 cm
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A Correct answer
Explanation

Arc length L = (theta/360) * 2 * pi * r. 44 = (84/360) * 2 * (22/7) * r. 44 = (7/30) * (44/7) * r. 44 = (44/30) * r. r = 30 cm.

AI explanation

The relationship between arc length, radius and the central angle is given by the formula Arc Length = (Angle / 360) * 2 * pi * r. Substituting the given values, we have 44 = (84 / 360) * 2 * (22/7) * r. Simplifying the equation gives 44 = (7/30) * 2 * (22/7) * r, which reduces to 44 = (44/15) * r. Solving for r gives a radius of 30 cm.

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