G.C.5 WORKSHEET #2 – Hamilton
Name: ________________________________
1
Aim: How do I find the length of an arc of a circle?
Do Now: Determine the missing information. If you do not have enough information to fill out a row, be sure
you can explain why.
Equation
(x - 2) + (y + 4)2 = 25
Center
Radius
(-2,-4)
6
Diameter
2
(x + 2)2 + (y - 4)2 = 25
5
(2,4)
36
Note: Circumference is the ______________________ of a circle. The circumference formula is C=2 r.
Task 1: Determine the circumference of the following circles.
G.C.5 WORKSHEET #2 – Hamilton
2
Task 2: Revisiting #1.
What is the circumference of this
circle? _____________________
What do we call AB? _________
Let’s say I start at point A and walk
around the circle to point B, how far
will I have walked? ______________
How did you know this?
We
call this distance
arc-length
1.
Determine
the arc the
length.
of arc AB.
What is the circumference of this
circle? _____________________
What other information are you
given in this problem besides the
radius?
How many degrees are in the
intercepted arc?
Let’s say I start at point C and walk
around the circle to point D, how far
will I have walked? ______________
We call this distance the arc length
of arc CD.
Summary:
G.C.5 WORKSHEET #2 – Hamilton
3
Task 3: Draw a diagram that represents the following situations and then solve the arc length, s.
a) Central Angle of 30,
radius of 3 cm
b) Central Angle of 90,
radius of 8 cm
c) Central Angle of 72,
radius of 10 cm
Diagram:
Diagram:
Diagram:
s = ____________
s = ____________
s = ____________
d) Central Angle of

4
rad . ,
e) Central Angle of
2
rad . ,
3
f) Central Angle of
radius of 12 cm
radius of 15 cm
radius of 10 cm
s = ____________
s = ____________
s = ____________
4
rad . ,
5
G.C.5 WORKSHEET #2 – Hamilton
4
Task 4: Determine the arc length of the following.
a)
b)
4π rad.
5
10 cm
s = ____________ (E)
c)
7π rad.
6
3 cm
s = ____________ (E)
d)
3π rad.
2
π rad.
6
4 cm
s = ____________ (E)
18 cm
s = ____________ (E)
4. Circle G has a radius of 7 cm. After computing an arc on circle G, Nancy finds the arc length to be 14 cm.
She exclaims, “The central angle must be 2 radians.” How did she know this?
5. Find the radius of a circle in which a central angle of 5 radians intercepts an arc length of 62.5 feet?
6. Find the measure (in radians) of a central angle that intercepts an arc of length 16 cm
in a circle of radius 8 cm.
Summary:
7. Find the measure (in radians) of a central angle that intercepts an arc of length 24 cm
in a circle of radius 10 cm.