Find the angle at which an arc of length 22 cm subtends at the centre of a circle of radius 15cm.  [Take $\pi = \frac{22}{7}$]

Analyze the question: We have an arc length (22 cm) and a radius (15 cm). We need the angle the arc subtends at the centre.

Concept: Arc length is a fraction of the circumference:

Arc length = (θ/360) × 2πr

So θ = (Arc length × 360) / (2πr)

Solution:

1. Substitute r = 15 and π = 22/7: 2πr = 2 × (22/7) × 15 = 660/7 cm

2. Substitute into the formula: θ = (22 × 360) / (660/7) θ = (22 × 360 × 7) / 660

3. Simplify: 22/660 = 1/30, so θ = (360 × 7) / 30 = 12 × 7 = 84°

Check: (84/360) × (660/7) = (7/30) × (660/7) = 660/30 = 22 cm ✓

Answer: B. 84°.

Tip: For arc problems, rearrange the formula to θ = (l × 360) / (2πr). When π = 22/7 and the radius is 15, look for cancellations like 22 with 660 to save time. You can also check any option by plugging it back in to see whether you get the arc length.