1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
1. Find the length of the hypotenuse of a right triangle that has legs 3 in. and 4 in. long.
2. The hypotenuse of a right triangle measures 17 in., and one leg measures 8 in. How long is the other leg?
3. To the nearest centimeter, what is the height of an equilateral triangle with sides 9 cm long?
5 in.
15 in.
8 cm

3. Problem of the Day
A rectangular box is 3 ft. by 4 ft. by 12 ft. What is the distance from a top corner to the opposite bottom corner?
13 ft

4. 8-3
Circles
Learn to find the circumference and area of circles.

5. Vocabulary
circle
radius
diameter
circumference

6. A circle is the set of points in a plane that are a fixed distance from a given point, called the center. A radius connects the center to any point on the circle, and a diameter connects two points on the circle and passes through the center.

7. d = 2r Radius Center The diameter d is twice the radius r. Diameter
Circumference
The circumference of a circle is the distance around the circle.

9. Remember!
Pi () is an irrational number that is often approximated by the rational numbers 3.14 and 22 7

10. Additional Example 1: Finding the Circumference of a Circle
Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .
A. Circle with a radius of 4 m
C = 2r
= 2(4)
= 8 m  25.1 m
B. Circle with a diameter of 3.3 ft
C = d
= (3.3)
= 3.3 ft  10.4 ft

11. Check It Out: Example 1
Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .
A. Circle with a radius of 8 cm
C = 2r
= 2(8)
= 16 cm  50.2 cm
B. Circle with a diameter of 4.25 in.
C = d
= (4.25)
= 4.25 in.  13.3 in.

13. Additional Example 2: Finding the Area of a Circle
Find the area of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .
A. Circle with a radius of 4 in.
A = r2 = (42)
= 16 in2  50.2 in2 d 2
= 1.65
B. Circle with a diameter of 3.3 m
A = r2 = (1.652)
=  m2  8.5 m2

14. Check It Out: Example 2
Find the area of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .
A. Circle with a radius of 8 cm
A = r2 =  (82)
= 64 cm2  cm2 d 2
= 1.1
B. Circle with a diameter of 2.2 ft
A = r2 =  (1.12)
= 1.21 ft2  3.8 m2

15. Additional Example 3: Finding the Area and Circumference on a Coordinate Plane
Graph the circle with center (–2, 1) that passes through (1, 1). Find the area and circumference, both in terms of  and to the nearest tenth. Use 3.14 for .
A = r2
C = d
= (32)
= (6)
= 9 units2
= 6 units
 28.3 units2
 18.8 units

16. Check It Out: Example 3
Graph the circle with center (–2, 1) that passes through (–2, 5). Find the area and circumference, both in terms of  and to the nearest tenth. Use 3.14 for . y
A = r2
C = d
(–2, 5)
= (42)
= (8) 4
= 16 units2
= 8 units
 50.2 units2
 25.1 units x
(–2, 1)

17. Additional Example 4: Measurement Application
A Ferris wheel has a diameter of 56 feet and makes 15 revolutions per ride. How far
would someone travel during a ride? Use for . 22 7
C = d =  (56)
Find the circumference.
 (56)  22 7 56 1 22 7
 176 ft
The distance is the circumference of the wheel times the number of revolutions, or about 176  15 = 2640 ft.

18. A second hand on a clock is 7 in long. What is
Check It Out: Example 4
A second hand on a clock is 7 in long. What is
the distance it travels in one hour? Use for . 22 7
C = d =  (14)
Find the circumference. 14 1 22 7 12 3 6 9
 (14)  22 7
 44 in.
The distance is the circumference of the clock times the number of revolutions, or about 44  60 = 2640 in.

19. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 19

20. Lesson Quiz
Find the circumference of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .
1. radius 5.6 m
11.2 m; 35.2 m
2. diameter 113 m
113 mm; mm
Find the area of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .
3. radius 3 in.
9 in2; 28.3 in2
4. diameter 1 ft
0.25 ft2; 0.8 ft2

21. Lesson Quiz for Student Response Systems
1. Find the circumference of a circle with a radius of 6.3 inches, both in terms of  and to the nearest tenth. Use 3.14 for .
A. 12.6 in.; 37.1 in.
B. 12.6 in.; 39.6 in.
C. 11.8 in.; 39.6 in.
D. 11.8 in.; 37.1 in. 21

22. Lesson Quiz for Student Response Systems
2. Find the circumference of a circle with diameter of 120 mm, both in terms of  and to the nearest tenth. Use 3.14 for .
A. 120 mm; mm
B. 240 mm; mm
C. 240 mm; mm
D. 120 mm; mm 22

23. Lesson Quiz for Student Response Systems
3. Find the of the circle with a radius of 2 mm, both in terms of  and to the nearest tenth. Use 3.14 for .
A. 4 mm; 6.3 mm
B. 4 mm; 12.6 mm
C. 2 mm; 6.2 mm
D. 2 mm; 12.6 mm 23