HG U6D5 Arc Lengths and Sectors Nov4 - Ali Yasseri | Library

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Lisa said that in the circle below 𝑚∠𝐷 = 77°.

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Harrison said that in the circle below the 𝑚∠𝐴 = 61°.

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Jenna stated that in the circle below 𝑚∠𝐶 + 𝑚∠𝐴 = 180°.

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Find the area of the shaded portion of each circle.
Area = _______ units2

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Find the length of the highlighted portion of the circle's circumference.
circumference = _______ units

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Circumference
Notes and Examples

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Round answers to the nearest tenth (try using π, not 3.14). Also, try leaving answers in terms of π.

Find the circumference of a circle with a radius of 20 cm.
Circumference = _______ cm (rounded)
Circumference = _______ π cm
(in terms π).

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In circle G with the measure of angle FGH = 60o and FG = 19 cm, find the length of arc FH. Round to the nearest hundredth.
Arc Length = _______ cm

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What is the difference in the length of the arc between circle E and circle D?
Round to the nearest hundredth.
Difference = _______ units

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In circle E with the measure of angle DEF = 60o and DE = 15 cm, find the area of the sector. Round to the nearest hundredth.
Area of Sector = _______ cm2

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Suppose a circle is divided into congruent slices. Match each number of slices with the resulting central angle measure of each slice.

Draggable item		Corresponding Item

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A circle of radius 12 units is divided into 8 congruent slices.
a. What is the arc length of each slice? _______ units
b. What is the area of each slice? _______ units2

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Diego says, “To find arc length, divide the measure of the central angle by 360. Then multiply that by the area of the circle.“ Do you agree with Diego? Show or explain your reasoning.

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The image shows a triangle. Sketch the inscribed and circumscribed circles for this triangle.

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Triangle ABC is shown with its inscribed circle drawn. The measure of angle ECF is 72 degrees. What is the measure of angle EGF? Explain or show your reasoning.
angle EGF = _______o 

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How do the values of x and y compare? Explain your reasoning.

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In the diagram, the measure of the arc from A to B not passing through C is 80o. What is the measure of angle ACB?

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A sector of a circle is the region enclosed by 2 radii. For the circle, find the area of the shaded sector and the length of the arc that outlines the sector. All units are centimeters. Give your answers in terms of π.
Area of Sector = _______ cm2
Arc Length = _______ cm
Give your answers in terms of π.

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A sector of a circle is the region enclosed by 2 radii. For the circle, find the area of the shaded sector and the length of the arc that outlines the sector. All units are centimeters. Give your answers in terms of π.
Area of Sector = _______ cm2
Arc Length = _______ cm
Give your answers in terms of π.

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A sector of a circle is the region enclosed by 2 radii. For the circle, find the area of the shaded sector and the length of the arc that outlines the sector. All units are centimeters. Give your answers in terms of π.
Area of Sector = _______ cm2
Arc Length = _______ cm
Give your answers in terms of π.

Draggable item		Corresponding Item
180o		8 slices
90o		6 slices
45o		5 slices
72o		3 slices
60o		4 slices
120o		2 slices