Question

the length of the arc of a quadrant of a circle of radius r is​

Answer 1

Answer:

The length of the arc of the quadrant is  $\pi r/2$

Step-by-step explanation:

• Consider an arc that makes an angle $\theta$  at the centre and the length of the arc is s.

• We know,s is related to the angle is $r \theta$  (s is simply proportional to   ) as r is constant.

• Now,note the angle of a quadrant is   ,i.e.,1/4 times that of a circle

• Thus,the legth of the arc would be as well 1/4 times that of the circumferance of a circle .

• Hence,the lentgh of the arc is  $\pi r/2$

Answer 2

Answer:

Length of the arc of a quadrant of a circle with radius r = πr/2

Step-by-step explanation:

• Length of the arc of a circle is with radius r and angle ∝ = ∝/360° × (2πr).
• The angle in a quadrant is 90°.

• So the length of arc in a quadrant will be 90°/ 360° × (2πr).

       = 1/4 × (2πr)

       = 1/2 ×πr.