Question

The radius of a certain circle is $30$ cm find the approximate length of an arc of this circle; if the length of the chord of the arc be $30$ cm

Answer 1

The radius is 30 cm and also the chord is also 30 cm

So the triangle formed by the two radii and the chord of length 30 cm will be equilateral.

Now each of its angle will be ${60}^{\circ }$

which can also be written as $\frac{\pi }{3}$.

Now to find length of arc we have $\theta$ = $\frac{l}{r}$ where l is length of arc .

implies $l=\theta r$

= $\frac{30\pi }{3}$

$=10\pi$

=31.4cm

the approximate length of an arc of this circle=31.4cm