A rope of length 10cm is used to form a sector of circle of radius 3.5cm. What is the size of the angle of the sector?

Step-by-step explanation:

The perimeter of the sector is equivalent to the length of the rope which is 10cm

Perimeter of the sector= 2 x radius + length of the arc

But the length of arc= radius x central angle in radian

10= 2(3.5)+ 3.5(central angle in radians)

10=7+3.5 (central angle in radians)

10–7=3.5(central angle)

3=3.5(central angle)  central angle =3/3.5=1.16 radians or pi radians  Angle in degrees =pi radians x 360 degrees/2pi radians =pi radians x 180 degrees/pi radians = 180 degrees

Therefore the central angle = 180 degrees because pi radians is half of the 2pi radians which is half of 360 degrees

 This sector shape is a semicircle because the central angle is 180 degrees

Check the Length of Arc for semicircle =3.5(pi radians)=3 meters

Perimeter of the sector = 2r + length of arc= 2(3.5)+3= 7+11=10 meters exactly the length of the rope.