An arc of length 7 cm on a circle subtends a central angle o

An arc of length 7 cm on a circle subtends a central angle of 35 degree, as shown below. Answer the following: Determine the central angle of the sector in radians. Angle Measure Determine the radius of the sector. Determine the area of the sector

Solution

Central angle of sector in radian

We know that 1 = 180^o

and it is given that central angle is 35^o,

Hence,

35^o = 1/180^o x 35

we also know that 1= 22/7

35^o = 22/7 x 35/180

=11/18

35^o = 0.610865 radian

Radius of the sector = s/

=7/0.5

=14(approx)

Here we take s which is central angle in radian as 0.5 approx to get answer in round figure.

Area of sector = /360^o x r²

Here = 35^o

A=35/360 x 22/7 x (14)²

r =14 (calculated above)

On Solving We get,

A = 98/15

A= 6.53 (approx)