SAT Math Multiple Choice Question 971: Answer and Explanation

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Question: 971

7.

Points A and B lie on circle C as shown. The measure of angle ACB is 120°. If the area of circle C is 81π square units, what is the length of minor arc AB?

  • A. 6π
  • B. 9π
  • C. 18π
  • D. 27π

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Additional Topics in Math / Geometry

Strategic Advice: The length of an arc is found by multiplying the circumference of the circle by the portion of the circumference that the arc represents.

Getting to the Answer: You know that the area of the circle is 81π. The area of a circle is given by A = πr2, so r = 9. This means the circumference of the circle, which is given by C = 2πr, is C = 2π(9) = 18π. Now, find the portion of the circumference that minor arc AB represents by writing the measure of the central angle that subtends the arc over 360° (the number of degrees in a full circle):. The arc represents one-third of the circumference, or 18π ÷ 3 = 6π, which is (A).

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