Holt CA Course 1

9-4 Circumference and Area

Warm Up

California StandardsCalifornia Standards

Lesson Presentation

PreviewPreview

Holt CA Course 1

9-4 Circumference and Area

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

Holt CA Course 1

9-4 Circumference and Area

MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

Also covered: MG3.2

California

Standards

Holt CA Course 1

9-4 Circumference and Area

circumference

Vocabulary

Holt CA Course 1

9-4 Circumference and Area

Radius

CenterDiameter

Circumference

The diameter d is twice the radius r.

dd = 2= 2rr

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

Holt CA Course 1

9-4 Circumference and Area

Holt CA Course 1

9-4 Circumference and Area

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

approximated by the rational numbers 3.14

and .227

Holt CA Course 1

9-4 Circumference and AreaAdditional 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 .

Holt CA Course 1

9-4 Circumference and AreaCheck It Out! 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 .

Holt CA Course 1

9-4 Circumference and Area

Holt CA Course 1

9-4 Circumference and AreaAdditional 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

Holt CA Course 1

9-4 Circumference and Area

B. circle with a diameter of 2.2 ft

A = r2 = (1.12)

= 1.21ft2 3.8 ft2

d2 = 1.1

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 = r2 = (82)

= 64cm2 201.0 cm2

A. circle with a radius of 8 cm

Holt CA Course 1

9-4 Circumference and AreaAdditional 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

Holt CA Course 1

9-4 Circumference and AreaCheck It Out! 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

Holt CA Course 1

9-4 Circumference and AreaAdditional 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.

Holt CA Course 1

9-4 Circumference and Area

12

3

6

9

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)

(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

Holt CA Course 1

9-4 Circumference and AreaLesson 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

11.2 m; 35.2 m

113 mm; 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

9 in2; 28.3 in2

0.25 ft2; 0.8 ft2