Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GRE score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
In the figure above, the circumference of the circle is equal to , and
[#permalink]
09 Dec 2022, 06:20
Expert Reply
00:00
Question Stats:
0% (00:00) correct
100% (02:23) wrong based on 5 sessions
HideShow
timer Statistics
Attachment:
GRe In the figure above, the circumference of the circle is equal to .jpg [ 11.41 KiB | Viewed 1377 times ]
In the figure above, the circumference of the circle is equal to 1/4 , and the arc PQR is equal to 1/4 of the total circumference. What is the area of the shaded region?
Re: In the figure above, the circumference of the circle is equal to , and
[#permalink]
11 Dec 2022, 04:00
Expert Reply
2
Bookmarks
OE
For most shaded area problem, use the formula shaded area = total area − unshaded area. Since the figure for the problem does not include a center for the circle, give the circle a center O. Draw one radius from the center O to point P, and another radius from O to point R to create central angle POR. Since arc PQR equals 1/4 of the total circumference, the central angle formed will be 1/4 of 360°; angle PQR is 90°. From the information in the problem you know that circumference = 8π, so r = 4. The triangle POR is an isosceles right triangle with legs of 4 and an area of 8. The area of the circle is equal to πr2, so the area of the circle is 16π. The total area taken up by the triangle and the shaded area together will be equal to 1/4 of the area of the circle, or 4π. The total area is 4π and the unshaded area is 8, so the shaded area is 4π − 8, which is choice (D).
_________________
In the figure above, the circumference of the circle is equal to , and
[#permalink]
11 Dec 2022, 07:23
1
Hi Carcass, I read the OE but got confused how do you get "From the information in the problem you know that circumference = 8π, so r = 4." The question said "In the figure above, the circumference of the circle is equal to 1/4 , and the arc PQR is equal to 1/4 of the total circumference. What is the area of the shaded region?"