Lessons 6.5 Circumferenceand 8.5 Area of a Circle

PI π = Ratio of Circumference to Diameter

HOMEWORK: Lesson 6.5/1-13 Lesson 8.5/1-10

Circumference

Pi () is approximately ≈ 3.14 (or 22/7)

Pi is exactly =

C =

Finding the CircumferenceYou can find the circumference of a circle by using the formula-

Circumference = π x diameterFor Example-

Circumference= π * 10C = 10π cm

C ≈ 10*3.14 C ≈ 31,4 cm

10cmexact

approx.

Example 1:

Solution:

The diameter of a circle is 3 centimeters. What is the circumference?

C = π dC = 3 π cm

C ≈ 9.42 cmC ≈ 3 (3.14) cm

exact

approx.

Example 2:The radius of a circle is 2 inches. What is the circumference? Solution:

C = 4 π in

C ≈ 4 * 3.14

C ≈ 12.56 in

exact

approx.

C = 2 π 2C = 2 π r

Example 3:

The circumference of a circle is 15.7 centimeters. What is the diameter?

Solution:

15.7 cm = πd

cm = d

d ≈

d≈ 5 cm

exact

approx.

Example 4:

The distance around a carousel is 21.98 yards. What is the radius?

C = 2 π r

21.98 = 2 π r

yds = r

≈ r

r≈ 3.5 ydsexact

approx.

Finding the AreaArea= π * radius2

Area= π * 72

= π * 49 A = 49 π (exact)

A 49 * 3.14 A 153.86 (approx)

A 49 * π (π button)

A 153.93804 153.94

(approx)

7cm

A=

6 cmr

Find the area of a circle given the diameter

12 cm

𝐴=𝜋 62

𝐴=36𝜋𝑐𝑚2

𝐴≈36∗3.14𝐴≈113.04𝑐𝑚2

𝐴=𝜋 𝑟2

Circumference Area

• If C = 25π cm• Find Area

25𝜋=2𝜋𝑟25𝜋=2𝜋𝑟25=2𝑟252

=22𝑟

12.5𝑐𝑚=𝑟

12.5𝑐𝑚=𝑟

𝐴=𝜋 𝑟2

𝐴=𝜋 12.52

𝐴≈490.63𝑐𝑚2exact

approx.

• If A = 144π • Find circumference

Circumference Area

144𝜋=𝜋 𝑟2

144𝜋=𝜋 𝑟2

144=𝑟 2

√144=𝑟12𝑐𝑚=𝑟

12𝑐𝑚=𝑟

𝐶=2𝜋 𝑟𝐶=2𝜋 12

𝐶=24𝜋 𝑐𝑚

𝐶 ≈75.36𝑐𝑚

exact

approx.

• If A = 200.96 • Find circumference

Circumference Area

200.96=𝜋𝑟 2

200.96=3.14 𝑟2

64=𝑟 2

8𝑐𝑚=𝑟

𝐶=2𝜋 8 cm

𝐶 ≈16∗3.14𝑐𝑚

𝐶 ≈50.24𝑐𝑚

200.963.14

=3.143.14

𝑟2

√64=𝑟8𝑐𝑚=𝑟

exact

approx.

Sketch and Solve• What is the circumference of a 12-inch pizza?

– C= πd– C= 12π in– C≈ 12*3.14 in– C≈ 37.68 in

• What is the surface area of the pizza?– A = π r=6 in– A=36 π – A ≈ 113.04

12 inexact

approx.

exact

approx.

• The distance around a carousel is 21.98 yards. What is the radius?– C=21.98yds– 21.98 = 2πr

– 3.5yds r• An asteroid hit the earth and created a huge round

crater. Scientists measured the distance around the crater as 78.5 miles. What is the diameter of the crater?– C=78.5yds– 78.5 = πd

– 25 miles d

The area of a circle Use π = 3.14 to find the area of the following circles:

A = πr22 cm

= 3.14 × 22

= 12.56 cm2

A = πr2

10 m= 3.14 × 52

= 78.5 m2

A = πr2

23 mm = 3.14 × 232

= 1661.06 mm2

A = πr2

78 cm= 3.14 × 392

= 4775.94 cm2

Finding the Area

A= π x r2

A= 36 πcA ≈ 113.04

A=121π A≈

A=4πA≈ 12.56

A=25πA≈ 78.5

A=4.84 πA≈ 15.20

A=100πA≈ 314

A=49π A≈153.86

A=32π ,A≈

exact

approx.