1. 10-5
Circles
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. The perimeter is multiplied by 5, and the area is multiplied by 25.
Course 1
10-5
Circles
Warm Up
The length and width of a rectangle are each multiplied by 5. Find how the perimeter and area of the rectangle change.
The perimeter is multiplied by 5, and the area is multiplied by 25.

3. Circles 10-5 Problem of the Day
Course 1
10-5
Circles
Problem of the Day
When using a calculator to find the height of a rectangle whose length one knew, a student accidentally multiplied by 20 when she should have divided by 20. The answer displayed was 520. What is the correct height?
1.3

4. Course 1
10-5
Circles
Learn to identify the parts of a circle and to find the circumference and area of a circle.

5. Insert Lesson Title Here
Course 1
10-5
Circles
Insert Lesson Title Here
Vocabulary
circle
center
radius (radii)
diameter
circumference pi

6. Course 1
10-5
Circles
A circle is the set of all points in a plane that are the same distance from a given point, called the center.
Center

7. Course 1
10-5
Circles
A line segment with one endpoint at the center of the circle and the other endpoint on the circle is a radius (plural: radii).
Radius
Center

8. Course 1
10-5
Circles
A chord is a line segment with both endpoints on a circle. A diameter is a chord that passes through the center of the circle. The length of the diameter is twice the length of the radius.
Radius
Center
Diameter

9. Additional Example 1: Naming Parts of a Circle
Course 1
10-5
Circles
Additional Example 1: Naming Parts of a Circle
Name the circle, a diameter, and three radii. L Z M N
The circle is circle Z.
LM is a diameter.
ZL, ZM, and ZN are radii.

10. Circles 10-5 Try This: Example 1
Course 1
10-5
Circles
Try This: Example 1
Name the circle, a diameter, and three radii. G H D I
The circle is circle D.
IG is a diameter.
DI, DG, and DH are radii.

11. Circles 10-5 The distance around a circle is called the circumference.
Course 1
10-5
Circles
The distance around a circle is called the circumference.
Circumference
Radius
Center
Diameter

12. Course 1
10-5
Circles
The ratio of the circumference to the diameter, , is the same for any circle. This
ratio is represented by the Greek letter , which is read “pi.” C d C d
= 

13. Course 1
10-5
Circles
The decimal representation of pi starts with and goes on forever without repeating. We estimate pi using either 3.14 or 22 7
The formula for the circumference of a circle is C = d, or C = 2r.

14. Course 1
10-5
Circles
Additional Example 2A: Using the Formula for the Circumference of a Circle
Find the missing value to the nearest hundredth. Use 3.14 for pi.
A. d = 11 ft; C = ?
11 ft
C = d
Write the formula.
C  3.14 • 11
Replace  with 3.14 and d with 11.
C  ft

15. Course 1
10-5
Circles
Additional Example 2B: Using the Formula for the Circumference of a Circle
Find each missing value to the nearest hundredth. Use 3.14 for pi.
B. r = 5 cm; C = ?
5 cm
C = 2r
Write the formula.
C  2 • 3.14 • 5
Replace  with 3.14 and r with 5.
C  31.4 cm

16. Course 1
10-5
Circles
Additional Example 2C: Using the Formula for the Circumference of a Circle
Find each missing value to the nearest hundredth. Use 3.14 for pi.
C. C = cm; d = ?
C = d
Write the formula.
21.98  3.14d
Replace C with and  with 3.14. d
_______ 
Divide both sides by 3.14.
7.00 cm  d

17. Circles 10-5 Try This: Example 2A
Course 1
10-5
Circles
Try This: Example 2A
Find the missing value to the nearest hundredth. Use 3.14 for pi.
A. d = 9 ft; C = ?
9 ft
C = d
Write the formula.
C  3.14 • 9
Replace  with 3.14 and d with 9.
C  ft

18. Circles 10-5 Try This: Example 2B
Course 1
10-5
Circles
Try This: Example 2B
Find each missing value to the nearest hundredth. Use 3.14 for pi.
B. r = 6 cm; C = ?
6 cm
C = 2r
Write the formula.
C  2 • 3.14 • 6
Replace  with 3.14 and r with 6.
C  cm

19. Circles 10-5 Try This: Example 2C
Course 1
10-5
Circles
Try This: Example 2C
Find each missing value to the nearest hundredth. Use 3.14 for pi.
C. C = cm; d = ?
C = d
Write the formula.
 3.14d
Replace C with and  with 3.14. d
_______ 
Divide both sides by 3.14.
6.00 cm  d

20. Course 1
10-5
Circles
The formula for the area of a circle is A = r2.

21. Additional Example 3: Using the Formula for the Area of a Circle
Course 1
10-5
Circles
Additional Example 3: Using the Formula for the Area of a Circle
Find the area of the circle. Use for pi.
d = 42 cm; A = ? 22 7
42 cm
A = r2
Write the formula to find the area.
r = d ÷ 2
The length of the diameter is twice the length of the radius.
r = 42 ÷ 2 = 21
A  • 212 22 7
Replace  with and r with 21. 22 7 __
A  • 441 22 7 __ 63
Use the GCF to simplify. 1
A  1,386 cm2
Multiply.

22. Circles 10-5 Try This: Example 3
Course 1
10-5
Circles
Try This: Example 3
Find the area of the circle. Use for pi.
d = 28 cm; A = ? 22 7
28 cm
A = r2
Write the formula to find the area.
r = d ÷ 2
The length of the diameter is twice the length of the radius.
r = 28 ÷ 2 = 14
A  • 142 22 7
Replace  with and r with 14. 22 7 __
A  • 196 22 7 __ 28
Use the GCF to simplify. 1
A  616 cm2
Multiply.

23. Insert Lesson Title Here
Course 1
10-5
Circles
Insert Lesson Title Here
Lesson Quiz
Find the circumference and area of each circle. Use 3.14 for .
3. Find the area of a circle with a diameter of 20 feet. Use 3.14 for .
3 in.
8 in.
C = in.
C = in.
A = in2
A = in2
314 ft2