SAT Practice Questions: Circle Arcs and Sectors

By Ron Woldoff

The SAT Math exam may ask you to deal with, not a whole circle, but only part of it. For example, you may be asked to find the length of an arc (which is part of the circumference of a circle) or the area of a sector (which is part of the area of a circle).

The following practice questions ask you to find the area of a sector as a fraction of the circle, and the circumference of a circle based on the length of an arc.

Practice questions

In the following figure, point O is the center of the circle.


  1. What fraction of the circle is minor arc AOB?
  2. If the length of minor arc AOB is
    what is the circumference of the circle?

Answers and explanations

  1. The correct answer is Choice (C).
    The entire circle is 360 degrees. Place the 30-degree angle over 360 degrees and reduce it to 1/12.
  2. The correct answer is Choice (D).
    If minor arc AOB is 1/12 of the circle
    then 1/12 of the circle is