10-1 Circles and Circumference. A circle is the set of all points in a plane that are the same...

10-1 Circles and Circumference

A circle is the set of all points in a plane that are the same distance from a given point, called the center.

Center

10-1Circles and Circumference

A line segment with one endpoint at the center of the circle and the other endpoint on the circle is a radius (plural: radii).

CenterRadius

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A diameter is a line segment that passes through the center of the circle and has both endpoints on the circle. The length of the diameter is twice the length of the radius.

CenterRadius

Diameter

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Additional Example 1: Naming Parts of a Circle

Name the circle, a diameter, and three radii.

NThe circle is circle Z.

LM is a diameter.

ZL, ZM, and ZN are radii.

M

ZL

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Check It Out: Example 1

Name the circle, a diameter, and three radii.

The circle is circle D.

IG is a diameter.

DI, DG, and DH are radii.

G

H

DI

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The distance around a circle is called the circumference.

CenterRadius

Diameter

Circumference

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The ratio of the circumference to the diameter, , is the same for any circle. This

ratio is represented by the Greek letter , which is read “pi.”

Cd

Cd

=

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The formula for the circumference of a circle is C = d, or C = 2r.

The decimal representation of pi starts with 3.14159265 . . . and goes on forever without repeating. We estimate pi using either 3.14

or .22 7

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Additional Example 2: Application

A skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding to 3.

C = d

C 3 • 8

C 24 ft

Write the formula.

Replace with 3 and d with 8.

8 ft

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Check It Out: Example 2

A second skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding to 3.

C = d

C 3 • 14

C 42 yd

Write the formula.

Replace with 3 and d with 14.

14 yd

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Additional Example 3A: Using the Formula for the Circumference of a Circle

Find the missing value to the nearest hundredth. Use 3.14 for pi.

d = 11 ft; C = ?

C = d

C 3.14 • 11

C 34.54 ft

Write the formula.

Replace with 3.14 and d with 11.

11 ft

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Additional Example 3B: Using the Formula for the Circumference of a Circle

Find each missing value to the nearest hundredth. Use 3.14 for pi.

r = 5 cm; C = ?

C = 2r

C 2 • 3.14 • 5

C 31.4 cm

Write the formula.

Replace with 3.14 and r with 5.

5 cm

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Additional Example 3C: Using the Formula for the Circumference of a Circle


C = 21.98 cm; d = ?

C = d

21.98 3.14d

7.00 cm d

Write the formula.

Replace C with 21.98 and with 3.14.

21.98 3.14d_______ _______

3.14 3.14 Divide both sides by 3.14.

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Check It Out: Example 3A

Find the missing value to the nearest hundredth. Use 3.14 for pi.

d = 9 ft; C = ?

C = d

C 3.14 • 9

C 28.26 ft

Write the formula.

Replace with 3.14 and d with 9.

9 ft

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Check It Out: Example 3B


r = 6 cm; C = ?

C = 2r

C 2 • 3.14 • 6

C 37.68 cm

Write the formula.

Replace with 3.14 and r with 6.

6 cm

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Check It Out: Example 3C


C = 18.84 cm; d = ?

C = d

18.84 3.14d

6.00 cm d

Write the formula.

Replace C with 18.84 and with 3.14.

18.84 3.14d_______ _______

3.14 3.14 Divide both sides by 3.14.

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Lesson Quiz

Find the circumference of each circle. Use 3.14 for .

1. 2.

3. Find the circumference of a circle with

diameter of 20 feet. Use 3.14 for .

C = 25.12 in.

Insert Lesson Title Here

C = 18.84 in.

8 in.

62.8 ft

3 in.

Course 1


10-1 Circles and Circumference. A circle is the set of all points in a plane that are the same...

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