Plugging the radius into the formula, C = 2πr = 2π (3) = 6π.
Arc Length
An arc is part of a circle’s circumference. An arc contains two endpoints and all the points on the circle between the endpoints. By picking any two points on a circle, two arcs are created: a major arc, which is by definition the longer arc, and a minor arc, which is the shorter one.
Since the degree of an arc is defined by the central or inscribed angle that intercepts the arc’s endpoints, you need only know the measure of either of those angles and the measure of the radius of the circle to calculate the arc length. The arc length formula is:
where
n is the measure of the degree of the arc, and
r is the radius. The formula could be rewritten as arc length =
n⁄
360 
C, where
C is the circumference of the circle.
A Math IC question might ask:
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Circle D has radius 9. What is the length of arc AB? |
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In order to figure out the length of arc
AB, you need to know the radius of the circle and the measure of
, which is the inscribed angle that intercepts the endpoints of
AB. The question tells you the radius of the circle, but it throws you a little curveball by not providing you with the measure of
. Instead, the question puts
in a triangle and tells you the measures of the other two angles in the triangle. Using this
information you can figure out the measure of
. Since the three angles of a triangle must add up to 180º, you know that:
Since angle c is an inscribed angle, arc AB must be 120º. Now you can plug these values into the formula for arc length
Area of a Circle
The area of a circle depends on the radius of the circle. The formula for area is:
where r is the radius. If you know the radius, you can always find the area.
Area of a Sector
A sector of a circle is the area enclosed by a central angle and the circle itself. It’s shaped like a slice of pizza. The shaded region in the figure below is a sector:
The area of a sector is related to the area of a circle the same way that the length of an arc is related to circumference. To find the area of a sector, simply find what fraction of 360º the sector comprises and multiply this fraction by the area of the circle.
where n is the measure of the central angle which forms the boundary of the sector, and r is the radius.
Try to find the area of the sector in the figure below:
The sector is bounded by a 70º central angle in a circle whose radius is 6. Using the formula, the area of the sector is:
Polygons and Circles
You could potentially see a question or two on the Math IC that involve polygons and circles in the same figure. Here’s an example:
