A circular playground has radius $7 cm$ . Find the length of the arc subtended by a central angle of $6 0^{\circ}$ .

easy 1 mark Class 10 · Mathematics · Areas Related to Circles

Answer

Arc length

= \frac{7 π}{3} cm

The correct answer is Arc length $= \frac{7 π}{3} cm$ — Simplify: $\frac{1}{6} \times 2 = \frac{1}{3}$ , giving arc $= \frac{7 π}{3} cm$ .

Step-by-step solution

Write the formula for arc length: $arc = \frac{θ}{360} \times 2 π r$ where $θ$ is in degrees.
Substitute $θ = 6 0^{\circ}$ , $r = 7 cm$ into the formula.
Compute $\frac{60}{360} = \frac{1}{6}$ , so arc $= \frac{1}{6} \times 2 π \times 7$ .
Simplify: $\frac{1}{6} \times 2 = \frac{1}{3}$ , giving arc $= \frac{7 π}{3} cm$ .

Common mistake: Using

2 π

instead of

36 0^{\circ}

for the angle conversion.

Concept tested: Arc length