SAT Math Multiple Choice Practice Question 563: Answer and Explanation

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Question: 563


In the figure above, is the diameter of the circle with center O. The shaded portion of the figure has an area of 25π and is the area of the entire circle. What is the length of arc RST ?

A. 15π
B. 25π
C. 30π
D. 112.5π
E. 125π

Correct Answer: A


A Arc RST is half the circumference of the circle. Finding the radius is key to any circle question. The question states that the area of the shaded portion of the circle is 25π and is of the circle, so we know that the whole circle has an area of 9(25π) or 225π. Now we can use the area formula to get the radius: πr2 = 225π, so r = 15. The formula for the circumference of a circle is 2πr, so the circumference of the whole circle is 30π, and since arc RST is half the circumference, its length is 15π, answer A.

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