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.
Apr 25Crafting an Impactful Resume: Balancing Detail with Brevity
10:00 AM EDT
-10:30 AM EDT
Showcase your achievements through impactful storytelling! Get ready for an LIVE session on April 25, Learn how to craft compelling narratives on your resume that resonate with admission committees.
Apr 26Get a Top GRE Score with Target Test Prep
12:00 PM EDT
-01:00 PM EDT
The Target Test Prep course represents a quantum leap forward in GRE preparation, a radical reinterpretation of the way that students should study. In fact, more and more Target Test Prep students are scoring 329 and above on the GRE.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If each of the 4 circles above has radius 1,
[#permalink]
29 May 2018, 05:25
29 May 2018, 05:25
1
00:00
Question Stats:
92% (01:14) correct
7% (01:27) wrong based on 14 sessions
Hide Show timer Statistics
If each of the 4 circles above has radius 1, what is the area of the shaded region?
A) 1 – π/4
B) 2 – π/4
C) 2 – π/2
D) 4 – π
E) 4 – 2π
Re: If each of the 4 circles above has radius 1,
[#permalink]
29 May 2018, 23:38
29 May 2018, 23:38
2
In these four identical circles let us assume the center of the circle from left uppermost to left bottom most are a,b,c and d respectively
If we connect the center of the 4 circles we will get a square. Each side of the square will be of length 2
Now, the area of the square would be \(2 *2 = 4\)
We are required to find the area of the shaded region hence we should reduce the portion of the circle enclosed within the square that is not shaded.
Since the side of the square are at 90 degrees to each other we know that there are 4 right triangles within the square enclosed in the circle.
For this we should find the area of 4 sectors that are not shaded.
The area of each sector would be equal to the other three sector.
area of 1 sector = \(\frac{90}{360}\) * ∏ * \(r^2 = \frac{1}{4} *\) ∏ as radius = 1
for 4 sectors area would be \(\frac{1}{4} *\) ∏ \(* 4\) = ∏
Therefore, area of the shaded region = 4 - ∏
option D
If we connect the center of the 4 circles we will get a square. Each side of the square will be of length 2
Now, the area of the square would be \(2 *2 = 4\)
We are required to find the area of the shaded region hence we should reduce the portion of the circle enclosed within the square that is not shaded.
Since the side of the square are at 90 degrees to each other we know that there are 4 right triangles within the square enclosed in the circle.
For this we should find the area of 4 sectors that are not shaded.
The area of each sector would be equal to the other three sector.
area of 1 sector = \(\frac{90}{360}\) * ∏ * \(r^2 = \frac{1}{4} *\) ∏ as radius = 1
for 4 sectors area would be \(\frac{1}{4} *\) ∏ \(* 4\) = ∏
Therefore, area of the shaded region = 4 - ∏
option D
Attachments
circles.png [ 34.89 KiB | Viewed 2088 times ]
Re: If each of the 4 circles above has radius 1,
[#permalink]
30 May 2018, 16:27
30 May 2018, 16:27
Expert Reply
Outstanding explanation.
It should be put as sticky "answer of the month".
Regards
It should be put as sticky "answer of the month".
Regards
