Finding the radius or Finding the radius or ѳѳ

Steps to find Steps to find the radius or the radius or ѳѳ

Bring 360 up and multiplyBring 360 up and multiply

Multiply what you can on the rightMultiply what you can on the right

Divide left side by right sideDivide left side by right side

ExamplesExamples

A circle has a central angle of 86A circle has a central angle of 86⁰⁰ and an arc length of 26. Find the and an arc length of 26. Find the radius.radius.

What do you need first? What do you need first? The formula!

Example ContinuedExample Continued

Now follow the steps1. Bring 360 up and multiply

2. Multiply what you can on the right

3. Divide left side by right side

Another ExampleAnother Example

What do we know from the question?

Plug it in

Another ExampleAnother ExampleContinuedContinued

Follow the steps

Uh oh, we don’t want to solve for r² so how do we solve for r?

r = 5.65

More examplesMore examples

72000 = Π10²ѳ

72000 = 314.159ѳ Ѳ= 229.18

Last ExampleLast Example

A circle has an arc length of 45 and A circle has an arc length of 45 and a radius of 18, what is the a radius of 18, what is the ѳѳ??

16200 = 2Π18ѳ

16200 = 113.1ѳ Ѳ = 143.0

6. The area of sector AOB is 48π and 270m AOB . Find the radius of ○O.

m

360πr2Area of a sector =

270

360πr248π =

3

4r248 =

4

3

4

3

16

r264 =

r = 8

9

4 40m AOB 7. The area of sector AOB is and . Find the radius of ○O.

m

360πr2Area of a sector =

40

360πr2 π =

9

41

9r2 =

9

4

9

1

9

1

r2 =81

4

r = 9

2

SectionSectionssLet’s talk Let’s talk

pizzapizza

AREA OF SECTIONAREA OF SECTION = = AREA OF SECTOR – AREA OF SECTOR – AREA OF AREA OF TRIANGLETRIANGLE

¼ ¼ ππ r² - r² - ½ bh½ bh

Area of sectionArea of section = = area of sector – area of sector – area of area of triangletriangle ¼ ¼ ππ r² - r² - ½ bh½ bh

1010A OF = ½∙10∙10=A OF = ½∙10∙10= 5050

A OF SECTION = A OF SECTION =

2525ππ - 50 - 50A of circle = A of circle = 100100ππ

A OF = ¼ 100A OF = ¼ 100ππ == 2525ππ

60˚

8 612

60 430

OO

O

8. 9. 11.

Find the area of the shaded region. Point O marks the center of the circle.

10.

160

3π units2 9π - 18 units2 24π - 36√3 units2 8π - 8√3 units2

Some common fractions and Some common fractions and measures!measures!

Arc or Central Arc or Central Angle MeasureAngle Measure

Fraction of the Fraction of the CircleCircle

Arc or Central Arc or Central Angle MeasureAngle Measure

Fraction of the Fraction of the CircleCircle

3636oo 108108oo

1/61/6 5/65/6

120120oo 2/32/3

3030oo 11/1211/12

1/81/8 5/85/8

1/10

1/3

1/12

3/10

60o

45o

300o

240o

225o

330o