GRE Prep Club Daily Prep
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In the figure above, the quarter circle with center D has a radius of
[#permalink]
02 Feb 2022, 06:30
02 Feb 2022, 06:30
1
Expert Reply
3
Bookmarks
00:00
Question Stats:
59% (01:56) correct
40% (01:52) wrong based on 27 sessions
Hide Show timer Statistics
Attachment:
GRE quarter circle.jpg [ 8.62 KiB | Viewed 1632 times ]
In the figure above, the quarter circle with center D has a radius of 4 and rectangle ABCD has a perimeter of 20. What is the perimeter of the shaded region?
A \(20 - 8\pi\)
B \(10 + 2\pi\)
C \(12 + 2\pi\)
D \(12 + 4\pi\)
E \(4 + 8\pi\)
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: In the figure above, the quarter circle with center D has a radius of
[#permalink]
13 Feb 2022, 07:03
13 Feb 2022, 07:03
1
Expert Reply
The perimeter ABCE = AB + BC + EC + AE
From the question stem we know:
white area is a quarter of a circle with center D.
radius = 4 = DC = ED
1) Lets find EC, which will be 1/4th of the circumference of the circle.
Circumference = 2πr = 8π
EC = 8π *1/4 = 2π
2) Find BC.
We know CD = radius = 4 = AB
We know the perimeter is 20.
Perimeter = 2CD + 2BC
20 = 2*4 + 2BC
BC = 6
3) Lets plug in our values and determine the answer.
ABCE = AB + BC + EC + AE
AB = 4
BC = 6
EC = 2π
AE = ?
ABCE = 10 + 2π + AE
Only option is C since we know AE>0.
==> C
From the question stem we know:
white area is a quarter of a circle with center D.
radius = 4 = DC = ED
1) Lets find EC, which will be 1/4th of the circumference of the circle.
Circumference = 2πr = 8π
EC = 8π *1/4 = 2π
2) Find BC.
We know CD = radius = 4 = AB
We know the perimeter is 20.
Perimeter = 2CD + 2BC
20 = 2*4 + 2BC
BC = 6
3) Lets plug in our values and determine the answer.
ABCE = AB + BC + EC + AE
AB = 4
BC = 6
EC = 2π
AE = ?
ABCE = 10 + 2π + AE
Only option is C since we know AE>0.
==> C
Re: In the figure above, the quarter circle with center D has a radius of
[#permalink]
29 Apr 2024, 15:55
29 Apr 2024, 15:55
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
