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Arc Length and Area of Sectors

Jenni McIntire and Teresa Davis

This lab is to investigate arc length and area of sectors in a circle. To do this lab you will need to use the following formulas:

Investigation:
In Sketchpad, make the following construction.

Construct circle A.
Construct radii AB and AC.
Measure angle BAC, the circumference of the circle, and arc length of arc BC.

Find the ratio of the measure of the central angle to the measure of the whole circle. Find the ratio of the arc length to the circumference of the circle. What do you notice about these ratios?

Set up a formula to find the arc length of any arc of a circle.

On the same circle:

Select the arc BC and construct the arc sector interior
Measure the area of the circle and the area of the sector.

Find the ratio of the area of the secto to the area of the circle. What do you notice about these ratios?

Set up a formula to find the area of a sector of any circle.

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