PSAT Math Grid-Ins Question 23: Answer and Explanation

Question: 23

Note: Figure not drawn to scale.

Major arc PSR is the length of minor arc PQR. The length of major arc PSR is 6π units. What is the radius of the circle?

Correct Answer: 5.25

Explanation:

5.25

The question asks for the radius of the circle. Start by translating English to math. Major arc PSR is the length of minor arc PQR means = . Since is 6π, substitute for to get 6π = . Multiply both sides by 3 to cancel out the fraction to get 18π = 4. Divide both sides by 4 to get = , or = 4.5π. The two arcs, and , add up to the circumference of the circle, so C = 6π + 4.5π = 10.5π. Since C = 2πr, the radius of the circle is 5.25. The correct answer is 5.25.