1. 6-4
Circles
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

2. Pre-Algebra
6-4
Circles
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. 6-4
Circles
Learn to find the area and circumference 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 (p) 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 = 2pr
= 2p(4)
= 8p m  25.1 m
B. Circle with a diameter of 3.3 ft
C = pd
= p(3.3)
= 3.3p ft  10.4 ft

11. Try This: 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 = 2pr
= 2p(8)
= 16p cm  50.2 cm
B. Circle with a diameter of 4.25 in.
C = pd
= p(4.25)
= 4.25p in.  13.3 in.

13. Additional Example 2: Finding the Area of a Circle
Find the area of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p.
A. Circle with a radius of 4 in.
A = pr2 = p(42)
= 16p in2  50.2 in2 d 2
= 1.65
B. Circle with a diameter of 3.3 m
A = pr2 = p(1.652)
= p m2  8.5 m2

14. Try This: Example 2
Find the area of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p.
A. Circle with a radius of 8 cm
A = pr2 = p(82)
= 64p cm2  cm2 d 2
= 1.1
B. Circle with a diameter of 2.2 ft
A = pr2 = p(1.12)
= 1.21p 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 p and to the nearest tenth. Use 3.14 for p.
A = pr2
C = pd
= p(32)
= p(6)
= 9p units2
= 6p units
 28.3 units2
 18.8 units

16. Try This: Example 3
Graph the circle with center (–2, 1) that passes through (–2, 5). Find the area and circumference, both in terms of p and to the nearest tenth. Use 3.14 for p. y
A = pr2
C = pd
(–2, 5)
= p(42)
= p(8) 4
= 16p units2
= 8p units
 50.2 units2
 25.1 units x
(–2, 1)

17. Additional Example 4: Measurement Application22 7
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 p.
C = pd = p(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. Find the circumference.
Try This: Example 4
A second hand on a clock is 7 in long. What is the distance it travels in one hour? Use for p. 22 7
C = pd = p(14)
Find the circumference.
 (14)  22 7 14 1 22 7 12 3 6 9
 44 in.
The distance is the circumference of the clock times the number of revolutions, or about 44  60 = 2640 in.

19. 1. radius 5.6 m 11.2p m; 35.2 m 2. diameter 113 m 113p mm; 354.8 mm
Lesson Quiz
Find the circumference of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p.
1. radius 5.6 m
11.2p m; 35.2 m
2. diameter 113 m
113p mm; mm
Find the area of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p.
3. radius 3 in.
9p in2; 28.3 in2
4. diameter 1 ft
0.25p ft2; 0.8 ft2