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Warm Up

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Warm Up

California Standards

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?

5 in.

15 in.

8 cm

California

Standards

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

Vocabulary

circumference

Circumference

Radius

Center

The diameter d is twice the radius r.

Diameter

d= 2r

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

22

7

Remember!

Pi () is an irrational number that is often approximated by the rational numbers 3.14 and .

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 = 2r

= 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

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 = 2r

= 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.

d

2

= 1.65

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

B. circle with a diameter of 3.3 m

A = r2 = (1.652)

= 2.7225 m2 8.5 m2

d

2

= 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. circle with a radius of 8 cm

A = r2 = (82)

= 64 cm2 201.0 cm2

B. circle with a diameter of 2.2 ft

A = r2 = (1.12)

= 1.21 ft2 3.8 ft2

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 .

C = d

A = r2

= (6)

= (32)

= 6 units

= 9 units2

18.8 units

28.3 units2

y

(–2, 1)

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 .

A = r2

C = d

(–2, 5)

= (42)

= (8)

= 16 units2

4

= 8 units

50.2 units2

25.1 units

x

22

7

22

7

(56)

56

1

22

7

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 .

Find the circumference.

C = d = (56)

176 ft

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

22

7

12

22

7

(14)

9

3

14

1

22

7

6

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 .

C = d = (14)

Find the circumference.

44 in.

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

Lesson Quiz

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

11.2 m; 35.2 m

1. radius 5.6 m

2. diameter 113 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.

9 in2; 28.3 in2

0.25 ft2; 0.8 ft2

4. diameter 1 ft