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Isaac Newton is one of the most famous scientists of all time, and His book
Now, you can assess your options. In this case, you need to find the value of r (the radius of the shaded circle) to calculate the area of the circle. You are given that the area of the large semicircle is 24, or in other words, the area of the circle (with A-B) as the diameter is 48. At this point you need to be very careful how you proceed. As long as you don't make any algebra errors, there are several ways to solve this problem, but some of them are much easier than others. You know that the area of the semicircle is 24 and you are looking for the area of the smaller circle. You also know that R (the radius of the semicircle) is twice what r (the radius of the shaded circle) is. Now, you can write the following formulas
Note that all you have above is the area of the semicircle (which is the area of a circle with radius R=2r divided by 2). Since you know that the area of the semicircle is equal to 24 you could solve the formula for r and then calculate the area of the shaded circle. However, notice that you already have the area of the circle calculated above, it's just being multiplied by 2. So instead you can write the following
Remember to loop back and verify that you have answered the bottom line. Recall that at the beginning you defined r as the radius of the shaded circle and R as the radius of the semicircle. Now look at the answer choices and select the one that matches your answer.
(E) It cannot be determined from the information given.
The correct answer is (C)
on sat.collegeboard.org 56% of the responses were correct.
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