Question

Find the length of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30°

Answer 1

Formula for arc lenght:
$l = \frac{ \alpha }{360} 2r\pi$
Insert given data:
$l = \frac{30}{360} \times 2 \times 12cm \times \pi$
$l = 2\pi = 6.28cm$

Answer 2

Answer:

Let s be the length of the arc subtending an angle $\sf{\theta}^{c}$ at the centre of a circle of radius r.

Then,

$\\ \theta \: = \sf \: \frac{s}{r}$

Here,

• r = 12 cm.
• ∅ = 30°

$\\ \implies \sf \: \bigg(30 \times \frac{\pi}{180} \bigg) {}^{c} \\ \\ \\ \implies \sf \blue{ \bigg({ \frac{\pi}{6} } \bigg)^{c} }$

Therefore,

$\\ \theta = \sf \: \dfrac{s}{r} \\ \\ \\ \implies \sf \: \frac{\pi}{6} = \frac{s}{12} \\ \\ \\ \implies \sf \red{s = \frac{12\pi}{6} cm. }$