6-4 Circles

Course 3

Warm Up

Problem of the Day

Lesson Presentation

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?

Course 3

6-4 Circles

5 in.

15 in.

8 cm

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

Course 3

6-4 Circles

13 ft

Learn to find the area and circumference of circles.

Course 3

6-4 Circles

Course 3

6-4 Circles

circle

radius

diameter

circumference

Vocabulary

Course 3

6-4 Circles

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.

Course 3

6-4 Circles

Radius

CenterDiameter

Circumference

The diameter d is twice the radius r.

d = 2r

The circumference of a circle is the distance around the circle.

Course 3

6-4 Circles

Course 3

6-4 Circles

Remember!Pi () is an irrational number that is often

approximated by the rational numbers 3.14

and .227

Course 3

6-4 Circles

Additional Example 1: Finding the Circumference of a Circle

A. Circle with a radius of 4 m

C = 2r= 2(4)

= 8m 25.1 m

B. Circle with a diameter of 3.3 ft

C = d= (3.3)

= 3.3ft 10.4 ft

Find the circumference of each circle, both in terms of and to the nearest tenth. Use 3.14 for .

Course 3

6-4 Circles

Try This: Example 1

A. Circle with a radius of 8 cm

C = 2r= 2(8)

= 16cm 50.2 cm

B. Circle with a diameter of 4.25 in.

C = d= (4.25)

= 4.25in. 13.3 in.

Find the circumference of each circle, both in terms of and to the nearest tenth. Use 3.14 for .

Course 3

6-4 Circles

Course 3

6-4 Circles

Additional Example 2: Finding the Area of a Circle

A = r2 = (42)= 16in2 50.2 in2

A. Circle with a radius of 4 in.

Find the area of each circle, both in terms of and to the nearest tenth. Use 3.14 for .

B. Circle with a diameter of 3.3 m

A = r2 = (1.652)

= 2.7225 m2 8.5 m2

d2 = 1.65

Course 3

6-4 Circles

B. Circle with a diameter of 2.2 ft

A = r2 = (1.12)

= 1.21ft2 3.8 m2

d2 = 1.1

Try This: Example 2

Find the area of each circle, both in terms of and to the nearest tenth. Use 3.14 for .

A = r2 = (82)

= 64cm2 201.0 cm2

A. Circle with a radius of 8 cm

Course 3

6-4 Circles

Additional Example 3: Finding the Area and Circumference on a Coordinate Plane

A = r2

= (32)

= 9units2

28.3 units2

C = d

= (6)

= 6units

18.8 units

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

Course 3

6-4 Circles

Try This: Example 3

x

yA = r2

= (42)

(–2, 1)

= 16units2

50.2 units2

C = d

= (8)

= 8units

25.1 units

4

(–2, 5)

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

Course 3

6-4 Circles

Additional Example 4: Measurement Application

C = d = (56)

176 ft (56) 22 7

22 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 .

Find the circumference.

56 1

22 7

The distance is the circumference of the wheel times the number of revolutions, or about 176 15 = 2640 ft.

Course 3

6-4 Circles

12

3

6

9

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 .

22 7

C = d = (14)

(14) 22 7

Find the circumference.

44 in.

The distance is the circumference of the clock times the number of revolutions, or about 44 60 = 2640 in.

14 1

22 7

Course 3

6-4 Circles

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

2. diameter 113 m

11.2m; 35.2 m

113mm; 354.8 mm

Find the area of each circle, both in terms of and to the nearest tenth. Use 3.14 for .

3. radius 3 in.

4. diameter 1 ft

9in2; 28.3 in2

0.25ft2; 0.8 ft2