HG U6D5 Arc Lengths and Sectors Nov4

Last updated 12 months ago

23 questions

1

Library

HG U6D5 Arc Lengths and Sectors Nov4

Last updated 12 months ago

23 questions

1

1

Circumference
Notes and Examples

1

1

1

Draggable item		Corresponding Item

1

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.

1

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

1

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 

1

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

1

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.

1

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.

1

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.

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

True

False

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

True

False

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

True

False

1

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

1

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

1

Find the area of the shaded portion of each circle.
area = _______ squared units

1

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

Circumference
Notes and Examples

1

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).

1

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 18 inches.
Circumference = _______inches (rounded)
Circumference = _______ π inches
(in terms π).

1

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

Find the radius of a circle with a circumference of 124 feet.
radius = _______feet (rounded)
radius = _______ feet
(in terms π).

1

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

1

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

1

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

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
60o		8 slices
72o		6 slices
120o		5 slices
180o		3 slices
45o		4 slices
90o		2 slices

1

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

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.

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

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 

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

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?

20o

40o

80o

160o

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.

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.

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.

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

True

False

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

True

False

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

True

False

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

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

Find the area of the shaded portion of each circle.
area = _______ squared units

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

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).

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 18 inches.
Circumference = _______inches (rounded)
Circumference = _______ π inches
(in terms π).

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

Find the radius of a circle with a circumference of 124 feet.
radius = _______feet (rounded)
radius = _______ feet
(in terms π).

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

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

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

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

60o

8 slices

72o

6 slices

120o

5 slices

180o

3 slices

45o

4 slices

90o

2 slices

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

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?

20o

40o

80o

160o