Math 2
Lesson 6-2: π and Circumference of a Circle
Name ______________________________
Date _____________________________
Learning Goals:


I can define π as the ratio of a circle’s circumference to its diameter.
I can use algebra to demonstrate that because π is the ratio of a circle’s circumference to its diameter that the
formula for a circle’s circumference must be 𝐶 = 𝜋 ∙ 𝑑.
I. For the circles below, measure their diameters to the nearest 10th of a centimeter. Record the results
in the table below.
Circumference ʘE  20.420 cm
Circumference ʘA  ______________
C
M
A
E
F
B
Circumference ʘQ  30.473 cm
Circumference ʘL  ______________
S
H
L
G
Q
T
Circumference in cm (C)
Length of the diameter to the
nearest 10th of a cm (d)
Circumference divided by
diameter (Round to the
nearest 100th.)
Circle L
Circle A
Circle Q
Circle E
Mean of column:
OVER 
Page 2
Notes:
II. More information about π:
π is an irrational number which means
Examples of other irrational numbers:
Approximations for π:
3,
3 1/8,
3.14,
3.14159,
22/7
III. Exact and approximate answers:
Circle the expression which represents the exact circumference of a circle with a diameter of 8 units.
8 * 3.14
8π
8 * 3.14159
8 * 22/7
IV. Examples
1. Give the circumference of a circle with radius 23 cm.
Exact _____________
To the nearest 10th of a cm ____________
2. The circumference of a circle is given. Find the desired length.
a. 242 cm; diameter
b. 8.75 ft; radius
3. A 5-foot rope is attached to a metal stake that is driven into the ground. A large dog is tied to the
other end of the rope.
a. What is the extent to which the dog can roam in a circular fashion with the rope fully extended?
b. If the rope were increased by one foot, what would be the new distance?
4. Find the circumference of the circle if the square has a perimeter of 36 cm.
Page 3
Homework:
Show your work for the following problems. Label your answers with the appropriate units & round to the
nearest 100th.
1. The diagonal of the below square is 40 inches. Find the circumference of the circle.
2. A lawn sprinkler rotates 360 and sprays water 6 feet. What is the circumference of the region that the
sprinkler waters?
3. The figure below is composed of a semi-circle and a square. The area of the square is 256 square
inches. Find the perimeter of the figure.
4. A dog is on a 12-foot leash that is tied to a stake. The dog walks around in circles with the leash fully
extended. How far does the dog walk in one full rotation around the stake?
5. The circumference divided by the diameter is called
A. radius
B. Pythagoras
C. pi
D. apothem
6. The diameter of a circle is 7 ft. What is the circumference of the circle?
A. 3.5 ft.
B. 14 ft.
C. 21.99 ft.
D. 38.47 ft.
7. The radius of a circle is 14 in. What is the circumference of the circle?
A. 87.96 in.
B. 615.44 in.
C. 43.96in.
D. 21.98 in.
8. The circumference of a circle is 22 cm. What is the diameter?
A. 7 cm.
B. 69.08 cm.
C. 11 cm.
D. 3.5 cm.
9. Circle the expression that shows the exact circumference of a circle with diameter 18 miles.
18 * 3.14 miles
18π miles
36π miles
56.54866776 miles
OVER
Page 4
10. Find the length of the semicircular window below whose radius is 4 ft:
11. Pac Man’s mouth is open at a 90◦ angle. Find the perimeter of Pac Man if the radius (edge of his
mouth) is equal to 22 mm.
12. Answer the following questions:
A. How many points make up a circle? __________________________________
B. How many centers does a circle have? __________________________________
C. How many radii does a circle have? __________________________________
D. How many diameters does a circle have? __________________________________
E. How is the length of the radius related to the length of the diameter?
______________________________________________________________________
Write an equation using r and d that represents this relationship. _______________________
F. How is the length of the diameter related to the length of the radius?
______________________________________________________________________
Write an equation using r and d that represents this relationship. _______________________
G. How do you describe the circumference of a circle?