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.
Four semicircular arcs of length
[#permalink]
10 Jun 2021, 08:54
10 Jun 2021, 08:54
Expert Reply
1
Bookmarks
00:00
Question Stats:
67% (01:32) correct
32% (01:07) wrong based on 28 sessions
Hide Show timer Statistics
Four semicircular arcs of length 2π are joined to make the figure above. What is the area of the enclosed region?
A. \(8\pi\)
B. \(8 + 8\pi\)
C. \(16 + 8\pi\)
D. \(16 + 16\pi\)
E. \(24\pi\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Four semicircular arcs of length
[#permalink]
10 Jun 2021, 09:09
10 Jun 2021, 09:09
1
Carcass wrote:
Four semicircular arcs of length 2π are joined to make the figure above. What is the area of the enclosed region?
A. \(8\pi\)
B. \(8 + 8\pi\)
C. \(16 + 8\pi\)
D. \(16 + 16\pi\)
E. \(24\pi\)
If one SEMI-circle has a perimeter of 2π, then an ENTIRE circle must have a circumference of 4π
Circumference = (diameter)(π)
So, if the circumference of the circle is 4π, then the diameter of each circle is 4
This means the square in the middle of the figure must have area 16.
Now we need only find the area of 4 SEMIcircles.
If we combine 2 semicircles we get an entire circle.
So, if we combine 4 semicircles we get 2 entire circles.
Each circle has diameter 4, which means each circle has RADIUS 2
Area of a circle = π(radius²)
So, area of one circle = π(2²) = 4π
So, the area of TWO circles = 8π
So, the TOTAL area = 16 + 8π
Answer: C
Cheers,
Brent
gmatclubot
Re: Four semicircular arcs of length [#permalink]
10 Jun 2021, 09:09
Moderators:
