finding the radius or ѳ. steps to find the radius or ѳ bring 360 up and multiply bring 360 up and...
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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