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Preview. 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?

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Warm Up

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Warm up

Preview

Warm Up

California Standards

Lesson Presentation


Warm up

  • 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


Warm up

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


Warm up

Vocabulary

circumference


Warm up

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.


Warm up

22

7

Remember!

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


Warm up

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


Warm up

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.


Warm up

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


Warm up

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


Warm up

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


Warm up

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


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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.


Warm up

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.


Warm up

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


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