Arcs and Sectors

ID: biboz-diriv
Favorite
Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Geometry
Grade: 9-12
PreviewAnswer Key

19 questions

Arcs and Sectors

Classroom:
Due:
Student Name:
Date Submitted:
Problem 1

Suppose a circle is divided into congruent slices. Write the central angle that corresponds to the number of slices.

Choose from this bank of possible central angles. Not all of the angles will be used in the table: 15°15\degree, 30°30\degree, 45°45\degree, 60°60\degree, 72°72\degree, 75°75\degree, 90°90\degree, 120°120\degree, 135°135\degree, 180°180\degree

1) 2 slices

2) 3 slices

3) 4 slices

4) 5 slices

5) 6 slices

6) 8 slices

Problem 2

A circle of radius 12 units is divided into 8 congruent slices.

7) What is the area of each slice? Write your answer in terms of π\pi.

8) What is the arc length of each slice?

Problem 3

Diego says, “To find arc length, divide the measure of the central angle by 360. Then multiply that by the area of the circle.“

9) Is Diego correct?

True or false? Write below.

10) Show or explain your reasoning.

Problem 4

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

A template for answering this question. Ask your instructor for an alternative.

12) Compare and contrast the 2 circles.

Problem 5

Triangle ABCABC is shown with its inscribed circle drawn. The measure of angle ECFECF is 72 degrees.

A template for answering this question. Ask your instructor for an alternative.

13) What is the measure of angle EGFEGF?

14) Explain or show your reasoning.

Problem 6


A template for answering this question. Ask your instructor for an alternative.

15) How do the values of xx and yy compare?

a)

x>yx>y

b)

xx=yy

c)

xx<yy

d)

There is not enough information.

Problem 7

Points AA, BB, and CC are the corners of a triangular park. The park district is going to add a set of swings inside the park. The goal is to have the swings equidistant from the vertices of the park.

16) Find a location that meets this goal.

A template for answering this question. Ask your instructor for an alternative.

17) Explain or show your reasoning.

Problem 8

18) In the diagram, the measure of the arc from AA to BB not passing through CC is 80 degrees. What is the measure of angle ACBACB?

A template for answering this question. Ask your instructor for an alternative.
a)

20 degrees

b)

40 degrees

c)

80 degrees

d)

160 degrees

Problem 9

19) This solid has curved sides. All cross sections parallel to the base are squares measuring 3 units on each side. The height from the base to the top is 8 units. What is the volume of this solid?

A template for answering this question. Ask your instructor for an alternative.