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.
The circle with center D is drawn inside the circle with center C, as
[#permalink]
09 Jun 2023, 07:42
09 Jun 2023, 07:42
Expert Reply
00:00
Question Stats:
78% (01:02) correct
21% (01:07) wrong based on 14 sessions
Hide Show timer Statistics
Attachment:
GRE in the circle above.jpg [ 21.7 KiB | Viewed 1272 times ]
The circle with center D is drawn inside the circle with center C, as shown in the figure above. If CD = 3, what is the area of semicircle EAB ?
A. \(\frac{9}{2} \pi\)
B. \(9 \pi\)
C. \(12 \pi\)
D. \(18 \pi\)
E. \(36 \pi\)
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) Cracking the GRE Premium
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
Re: The circle with center D is drawn inside the circle with center C, as
[#permalink]
11 Jun 2023, 01:42
11 Jun 2023, 01:42
1
Since CD=3, DE also = 3
Now the radius of the bigger circle is CE= CD+ DE = 3+3 = 6
The area of the bigger circle = π(6)^2 = 36π
So, the area of the halfcircle EAB = 18 π
Ans: D
Posted from my mobile device
Now the radius of the bigger circle is CE= CD+ DE = 3+3 = 6
The area of the bigger circle = π(6)^2 = 36π
So, the area of the halfcircle EAB = 18 π
Ans: D
Posted from my mobile device
Re: The circle with center D is drawn inside the circle with center C, as
[#permalink]
11 Jun 2023, 04:00
11 Jun 2023, 04:00
Expert Reply
OE
The question asks for the area of semicircle EAB. The questions states that the circle with center D has a radius of 3 because CD = 3, which means that the diameter of the smaller circle is equal to 2 × 3 = 6. The radius of the larger circle with center C is the diameter of the smaller circle, which is equal to 6. So, the area of the larger circle is π6 2 = 36π. The area of semicircle EAB is equal to one half the area of the larger circle, so one half of 36π is 18π. The correct answer is (D).
The question asks for the area of semicircle EAB. The questions states that the circle with center D has a radius of 3 because CD = 3, which means that the diameter of the smaller circle is equal to 2 × 3 = 6. The radius of the larger circle with center C is the diameter of the smaller circle, which is equal to 6. So, the area of the larger circle is π6 2 = 36π. The area of semicircle EAB is equal to one half the area of the larger circle, so one half of 36π is 18π. The correct answer is (D).
