Arcs and Sectors

Arcs and Sectors

Let’s analyze portions of circles.

I can calculate lengths of arcs and areas of sectors in circles.

​Learning Target

Fill in the Blanks

Find the area of the shaded portion of the circle, where r=8. Leave your answer in terms of pi.

Fill in the Blanks

Find the length of the highlighted portion of the circle’s circumference., where r=8. Leave your answer in terms of pi.

Fill in the Blanks

Find the area of the shaded portion of the circle., where r=6. Leave your answer in terms of pi.

Fill in the Blanks

Find the length of the highlighted portion of the circle’s circumference, where r=6. Leave your answer in terms of pi.

Sector

The region inside a circle lying between two radii of the circle.

Sector

To calculate the area of a sector or the length of an arc, first find the fraction of the circle represented by the central angle of the arc or sector. Multiply this fraction by the circle’s area or circumference. (Theorem)

Open Ended

Find the area of the shaded sector and the length of the arc that outlines the sector.

Open Ended

Find the area of the shaded sector and the length of the arc that outlines the sector.

Open Ended

Find the area of the shaded sector and the length of the arc that outlines the sector.

Open Ended

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  degrees and the circle’s radius is  units. Use the diagram to tell Mai how to find the area of a sector and the length of an arc for any angle and radius measure.

Open Ended

The image shows a circle with a shaded sector.

Find the area of the shaded sector.

Find the length of the arc defined by the sector.

I can calculate lengths of arcs and areas of sectors in circles.

​Learning Target