# Arcs and Sectors

ID: fahak-bonig
Illustrative Mathematics, CC BY 4.0
Subject: Geometry
Standards: HSG-C.B.57.G.B.4HSG-C.BHSG-GMD.A.1HSA-SSE.A.1.b

14 questions

# Arcs and Sectors

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##### Math Talk: Fractions of a Circle

Solve each problem. Leave answers in terms of ﻿$\pi$﻿.

1) Find the area of the shaded portion of the circle.

2) Find the length of the highlighted portion of the circle’s circumference.

3) Find the area of the shaded portion of the circle.

4) Find the length of the highlighted portion of the circle’s circumference.

##### Sector Areas and Arc Lengths

A ﻿$\textbf{sector}$﻿ of a circle is the region enclosed by 2 radii.

For each 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 ﻿$\pi$﻿.

5) Find the area of the sector.

6) Find the arc length of the sector.

7) Find the area of the sector.

8) Find the arc length of the sector.

9) Find the area of the sector.

10) Find the arc length of the sector.

##### Build a Method

Mai says, “I know how to find the area of a sector or the length of an arc for central angles like 180 degrees or 90 degrees. But I don’t know how to do it for central angles that make up more complicated fractions of the circle.”

In the diagram, the sector’s central angle measures ﻿$\theta$﻿ degrees and the circle’s radius is ﻿$r$﻿ units.

11) Use the diagram to help Mai find a formula for the area of a sector shown.

Area of sector =

12) Use the diagram to help Mai find a formula for the length of the arc defined by the sector.

Length of arc =

This image shows a circle with radius and central angle measurements.

13) Find the area of the shaded sector.

14) Find the length of the arc defined by the sector.