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?[br][br]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?[br][br]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?[br][br]d. Try some other central angle measurements. Create a formula for finding the length of an arc with any central angle.[br][br]e. Create a formula for finding the area of a sector with any central angle.