Question

The measure of central angle of circle is 150° and the radius of circle is 21 cm. To find the length of the arc complete the following activity.

Length of arc = `l = θ/(360^circ) xx square`

= `(150^circ)/square xx square xx 22/7 xx 2`

= `square` cm

Answer 1

1. Formula box

The formula for the length of an arc is `θ/(360^circ) xx 2πr`.

Length of arc = `l` = \[\frac{θ}{360°} \times \boxed{2πr}\]

2. Substitution and Calculation boxes

Substitute the given values (θ = 150°, r = 21 cm and `π = 22/7`):

= \[\frac{150°}{360°} \times \boxed{21} \times \frac{22}{7} \times 2\]

= \[\boxed{55}\] cm

1. Write out the full expression:

`l = (150^circ)/(360^circ) xx 21 xx 22/7 xx 2`

2. Simplify the angle fraction:

`(150^circ)/(360^circ) = 5/12`

3. Simplify the radius and π fraction:

`21/7 = 3`

4. Multiply the remaining numbers:

`l = 5/12 xx 3 xx 22 xx 2`

= `5/12 xx 132` 

= 5 × 11

= 55 cm