Question

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the
arc is

Answer 1

Answer:

Hope this is helpful for you.

Answer 2

Given,

A circle of radius 21 cm with a subtends arc of an angle 60° at the centre.

To Find,

The length of the arc.

Solution,

$\setlength{\unitlength}{1.2mm}\begin{picture}\thicklines\qbezier(25.000,10.000)(33.284,10.000)(39.142,15.858)\qbezier(39.142,15.858)(45.000,21.716)(45.000,30.000)\qbezier(45.000,30.000)(45.000,38.284)(39.142,44.142)\qbezier(39.142,44.142)(33.284,50.000)(25.000,50.000)\qbezier(25.000,50.000)(16.716,50.000)(10.858,44.142)\qbezier(10.858,44.142)( 5.000,38.284)( 5.000,30.000)\qbezier( 5.000,30.000)( 5.000,21.716)(10.858,15.858)\qbezier(10.858,15.858)(16.716,10.000)(25.000,10.000)\put(25,30){\line(5, - 4){16}}\put(25,30){\circle*{1}}\put(24,32){\sf\large{O}}\put(15,40){\sf\large{Major Sector}}\put(5,14){\sf\large{A}}\put(25,30){\line(- 5, -4){16}}\put(43,14){\sf\large{B}}\put(14,16){\sf\large{Minor Sector}}\end{picture}$

Radius of the circle = 21 cm

Measure the angle formed = 60°

We know that,

Length of the arc =   θ/360° x 2πr

Taking π as 22/7 and substituting the values,

= $\dfrac{60}{360}\times2\times\dfrac{22}{7}\times21$

It can be simplified as →

$\dfrac{1}{6}\times2\times\dfrac{22}{7}\times21$

= 22 cm.

Therefore the length of the arc is 22 cm.

Formulas used:

→ Formula for length of an arc.