bell work: write 2 formulas for the circumference of a circle
TRANSCRIPT
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Bell Work:
Write 2 formulas for the circumference of a circle.
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Answer:
C = πD
C = 2πr
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LESSON 40: AREA OF A CIRCLE
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The area of a circle is related the the area of a square on the radius. The area of a circle is π times the area of a square on the radius. A formula for the area of a circle is
A = πr2
r
r
r2
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The area of a circle is related to the area of a square on its radius. The area is greater than the area of three of these squares but less than the area of four such squares.
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The area of the circle is π times the area of the square of the radius as we see from the formula A = πr.
2
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Example:
A circular table in the library has a diameter of 6 feet. If four students sit around the table, then each student has about how many square feet of work area?
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Answer:
A = 3.14(9 feet )
A ≈ 28.26 feet
2
2
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Example:
Express the answers to (a) and (b) in terms of π.
a) What is the circumference of this circle?
b) What is the area of this circle?
6 inches
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Answer:
a) Radius = 6 Diameter = 12
Circumference = 12π inches
b) Area = πr = π(6)
= 6π inches2
2 2
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A sector of a circle is a portion of the interior of a circle enclosed by two radii and an arc which is part of the circle.
The angle formed by the radii, called a central angle, determines the fraction of the area of the circle the sector occupies.
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Central Angle
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Practice:
A lawn sprinkler waters a circular portion of a yard. The radius of the circular portion is 7 feet. Calculate the area of the yard watered by the sprinkler to the nearest square foot.
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Answer:
22/7(7 feet)
= 22/7(49 feet )
≈154 feet
2
2
2
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Practice:
What effect does doubling the diameter of a circle have on the area of the circle?
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Answer:
Doubling the diameter doubles the radius. The radius is squared to calculate the area, so doubling the radius results in a circle with an area four times (2 ) as large.
2
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Practice:
Find the area of the sector. Express in terms of π.
45°
6 cmM
R
S
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Answer:
45°/360° = 1/8 of the circle
Area = πr
= π(4 cm)
= 16πcm
Area of sector = 1/8 16πcm
= 2πcm
2
2
2
2
2
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Practice:
Find the area of the sector. Express in terms of π.
16 cm
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Answer:
π(8 cm)
= 64πcm
Area of sector = ½(64πcm )
= 32πcm
2
2
2
2
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HW: Lesson 40 #1-30