# Arc Length Exploration

- Author:
- Ben Graber

An arc is a part of the outside of a circle (a fraction of the circumference). A sector is a two-dimensional section of the whole circle (like a piece of pie). Use the applet below to explore how to calculate the measurements of these parts of a circle.

a. If a circle sector is created by the portion of the circle between a 45 degree angle at the center of the circle, what fraction of the whole circle is this?
b. Find the circumference of the whole circle. If the arc is a fractional part of the whole circumference, how can we use the fraction found above to find the length of the arc?
c. Find the area of the whole circle. If the sector is a fraction of the whole circle, how can we use the fraction found above to find the area of the sector?
d. Try some other central angle measurements. Create a formula for finding the length of an arc with any central angle.
e. Create a formula for finding the area of a sector with any central angle.