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TODAY IN GEOMETRY…
Warm up: Writing equations of a circle
Learning Target : 11.4 You will find the arc length and circumferences of circles
Independent practice
WARM UP:1. Write the standard 2. Graph the equation: equation of the circle.
(1 ,0)
3
Center: Radius: ¿ 4
CIRCUMFERENCE OF A CIRCLE: The distance around a circle is found from the formula
𝑪=𝝅𝒅
We also know that:𝑑
𝑟 𝑟
𝑪=𝟐𝝅𝒓
PRACTICE: Find the indicated measure. Round answers to the nearest tenth.
1. Circumference of a circle 2. Radius of a circle with with radius 9 centimeters. circumference 26 meters.
PRACTICE: Find the indicated measure.
a. Find the circumference of a circle with diameter 5 inches. Find the diameter of a circle with circumference 17 feet.
b. A car tire has a diameter of 28 inches. How many revolutions does the tire make while traveling 500 feet?
ARC LENGTH: Part of the circumference
𝑨𝒓𝒄 𝑳𝒆𝒏𝒈𝒕𝒉𝒐𝒇 𝑨𝑩=𝒎𝑨𝑩𝟑𝟔𝟎°
∙𝟐𝝅 𝒓
𝑃
𝑟
𝑟𝐴
𝐵
Use equation for arc length
Substitute known values
Solve
EXAMPLE: Find the length of the red arc.
Use equation for arc length
Substitute known values
Solve
EXAMPLE: Find the length of the red arc.
Use equation for arc length
Substitute known values
Solve
PRACTICE: Find the length of the red arc.
Use equation for arc length
Substitute known values
Solve
PRACTICE: Find the length of .
Use equation for arc length
Substitute known values
Solve
EXAMPLE: Find the circumference of .
Equation of circumference
Use equation for arc length
Substitute known values
Solve
PRACTICE: Find the circumference of .
Equation of circumference
Use equation for arc length
Substitute known values Divide
Solve
PRACTICE: Find the circumference .
Use equation for arc length
Substitute known values Divide
Solve
PRACTICE: Find the radius .
HOMEWORK #8:
Pg. 749: 3-7, 11-13, 15-23
If finished, work on other assignments:
HW #1: Pg. 655: 3-20, 24-26, 30HW #2: Pg. 661: 3-14, 17, 23HW #3: Pg. 667: 3-15HW #4: Pg. 676: 3-16 Pg. 679: 40-46HW #5: Pg. 683: 3-13HW #6: Pg. 692: 3, 4, 6, 9-14HW #7: Pg. 702: 3-25