Question of the Day

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11/8 , 12/6

Oct
25
2014
12,538 responses
Question of the Day Statistics
Number Answered
Correct 4,320
Incorrect 8,218
34% correct

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

8-26-2013-M37909.png

The circle shown above has center O and a radius of length 5. If the area of the shaded region is 20 times pi, what is the value of x?

Answer Choices

Hint

You can figure out the area of the whole circle, since you know that the radius is five. From the area of the whole circle and the area of the shaded part, it is possible to find the measure of the angle that has its vertex at point O and is in the right triangle. Once you find that angle measure, you can find the value of  x.

Question of the Day

Can you answer today's question?

Register Next Tests:
11/8 , 12/6

Oct
25
2014
12,538 responses
Question of the Day Statistics
Number Answered
Correct 4,320
Incorrect 8,218
34% correct

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

8-26-2013-M37909.png

The circle shown above has center O and a radius of length 5. If the area of the shaded region is 20 times pi, what is the value of x?

Answer Choices

Answer

In order to find the value of x, you should first determine the measure of the angle that is located at point O in the right triangle. To determine this angle, you must calculate what fraction of the circle’s area is unshaded. The radius r of the circle is 5 and its area is pi times r^2, or 25 times pi. The area of the shaded region is 20 times pi, so the area of the unshaded region must be 5 times pi. Therefore, the fraction of the circle’s area that is unshaded is (5 times pi) over (25 times pi), or 1 over 5. A circle contains a total of  three hundred and sixty degrees of arc, which means that 1 over 5 of  360 degrees, or 72 degrees, is the measure of the angle at point O in the unshaded region. Since you now know that two of the three angles in the triangle measure 72 degrees and 90 degrees and that the sum of the measures of the three angles is always 180 degrees, the third angle must measure 18 degrees. Therefore, x = 18.