Question

area of sector of circle of radius 6cm is 9pi cm^2 . find the length arc of the corresponding arc of the circle is
a) 6pi cm
b) 3pi cm
c) 5pi cm
d) 8pi cm
​

Answer 1

Answer:

Option b

The arc length of the circle when the area of a sector of a circle of radius $6$cm is$9\pi cm^2$ is$3\pi cm$

Step-by-step explanation:

Given:

The area of a sector of a circle of radius $6$ cm is $9\pi cm^2$

We need to find the arc length

The area of a sector of a circle is $A=\frac{\alpha }{360^0}*\pi r^2$

Circumference of a sector of a circle is $C=\frac{\alpha }{360^0}*2\pi r$

From the area of a sector we get :

$9\pi =\frac{\alpha }{360^0}*\pi *6^2\\\\\frac{\alpha }{360^0}= \frac{9}{36} \\\\\frac{\alpha }{360^0}= \frac{1}{4}$

Substituting this in the circumference we get :

$C=\frac{\alpha }{360^0}*2\pi r\\\\C=\frac{1 }{4}*2*\pi *6\\\\C=3\pi$

Answer 2

• Answer 3π cm

Have. a. nice. day. hope. this. answer. help. you.