The sector area is 22 Find the radius of each 09 rad 100 Sol

The sector area is 22. Find the radius of each.

Solution

(a)

For sector angle given in radian :

Area of sector =A=(/2)×(r²)=½r²,with=0.9 rad.

A=½r²(0.9) = 0.45r²= 9r²/20

(20/9)A=r²

r=(20A/9) =(20)(A)/3

r =(20)(22)/3 = 6.992 units

(b) This looks simpler, with in degree°,

A=(/360)×(r²)

A=(100/360)× (22/7)r²

22=(5/18)(22/7)r²

(18×7)/5 = r²

r=18(7/5) = 5.02 units