An arc subtends an angle of 72$^o$ at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5 cm. [Take $\pi = \frac{22}{7}$]

Analyze the question: We need the length of an arc that subtends 72° at the centre of a circle of radius 3.5 cm.

Concept: Arc length is a fraction of the circumference. The fraction is the angle at the centre divided by 360°.

Arc length = (θ/360) × 2πr

Solution:

1. Fraction of the circle: 72/360 = 1/5

2. Circumference: 2πr = 2 × (22/7) × 3.5 = 2 × 22 × 0.5 = 22 cm

3. Arc length = (1/5) × 22 = 4.4 cm

Answer: The arc length is 4.

Tip: Simplify the angle fraction first. 72/360 = 1/5 makes the arithmetic much easier. Also, 3.5 = 7/2, so it cancels neatly with the 7 in π = 22/7. Always look for this kind of cancellation when the question says "take π = 22/7".