PSAT Math Multiple-Choice Question 81: Answer and Explanation

Question: 81

The circle shown above has its center at O. If x = 60 and the length of minor arc AB is 2π, what is the area of circle O?

• A. 36π
• B. 12π
• C. 6π
• D. 6

Correct Answer: A

Explanation:

A

The question asks for the area of the circle. The parts of a circle are directly proportional to one another. In this circle, the fraction of the central angle of 360° is the same as the fraction of the arc length of the total circumference. Set up the proportion , then plug in the given information to get . Cross-multiply to get 60(circumference) = 360(2π). Divide both sides by 60 to get circumference = 12π. Since the formula for circumference is 2πr, the radius of the circle is 6. Then, find the area using the formula πr². If r = 6, then the circle has an area of π(6)² = 36π. The correct answer is (A).