Question

 

Find the length of arc AB, round to the nearest tenth. 

	A.	6.5
	B.	8.3
	C.	13.1
	D.	14.2

 

Find the radius of circle A, if the area of the shaded region is 47.5 cm². 

	A.	7 cm
	B.	7.5 cm
	C.	8 cm
	D.	8.5 cm

 

How do you find the arc length of a central angle of a circle? 

	A.
	B.
	C.
	D.	none of the above

 

Answer 1

(1).

Calculate the length of the arc AB by using formula :

L = (C/360) * 2πr, where C = is the central angle of the arc in degrees, r = the radius of the arc.

Substitute C = 125, π = 22/7 ≅ 3.142 and r = 6 in the above formula.

AB = 125/360 * 2 * 22/7 * 6

     = 33000/2520

     ≅ 13.1 units.

The option C is correct.

Answer 2

(2).

Calculate the radius of the circle by using the sector area formula :

A = (C/360) * πr², where C = is the central angle of the arc in degrees, r = the radius of the arc.

Substitute A = 47.5 cm², C = 85 and π = 22/7 ≅ 3.142 in the above formula.

47.5 = 85/360 * 22/7 * r²

64 ≅ r²

r = ± 8.

Radius of the circle cannot be expressed with negative sign.

r = 8 cm.

The option C is correct.

Answer 3

(3).

Calculate the length of the arc by using formula : s = r * θ, where θ = is measured in radians, r = the radius of the circle.

The option C is correct.