# Arcs and Sectors

ID: biboz-diriv Illustrative Mathematics, CC BY 4.0
Subject: Geometry

19 questions

# Arcs and Sectors

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##### 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: ﻿$15\degree$﻿, ﻿$30\degree$﻿, ﻿$45\degree$﻿, ﻿$60\degree$﻿, ﻿$72\degree$﻿, ﻿$75\degree$﻿, ﻿$90\degree$﻿, ﻿$120\degree$﻿, ﻿$135\degree$﻿, ﻿$180\degree$﻿

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 ﻿$\pi$﻿.

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. 12) Compare and contrast the 2 circles.

##### Problem 5

Triangle ﻿$ABC$﻿ is shown with its inscribed circle drawn. The measure of angle ﻿$ECF$﻿ is 72 degrees. 13) What is the measure of angle ﻿$EGF$﻿?

14) Explain or show your reasoning.

##### Problem 6 15) How do the values of ﻿$x$﻿ and ﻿$y$﻿ compare?

a)

﻿$x>y$﻿

b)

﻿$x$﻿=﻿$y$﻿

c)

﻿$x$﻿<﻿$y$﻿

d)

There is not enough information.

##### Problem 7

Points ﻿$A$﻿, ﻿$B$﻿, and ﻿$C$﻿ 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. 17) Explain or show your reasoning.

##### Problem 8

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