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 below, ABC is a circular sector with center A.
[#permalink]
14 Mar 2019, 10:45
14 Mar 2019, 10:45
Expert Reply
3
Bookmarks
00:00
Question Stats:
87% (01:01) correct
12% (00:57) wrong based on 48 sessions
Hide Show timer Statistics
In the figure below, ABC is a circular sector with center A. If arc BC has length \(4\pi\), what is the length of AC?
#GREpracticequestion In the figure below, ABC is a circular .jpg [ 17.98 KiB | Viewed 7135 times ]
Attachment:
#GREpracticequestion In the figure below, ABC is a circular .jpg [ 17.98 KiB | Viewed 7135 times ]
Show: :: OA
24
Re: In the figure below, ABC is a circular sector with center A.
[#permalink]
20 Mar 2019, 16:51
20 Mar 2019, 16:51
1
Expert Reply
The measure of the central angle is 30 degrees. This means it is equal to \(\frac{30}{360} = \frac{1}{12}\) of the entire circle.
This means that the area of ABC is 1/12 of the circle's area, and the length of arc BC is 1/12 of the circumference of the circle.
Since arc BC = \(4\pi\), the total circumference must be \(12(4\pi) = 48\pi\).
The circumference is equal to \(2\pi r\), where r is the radius. So:
\(2\pi r = 48\pi\)
Divide by \(2\pi\):
\(r = 24\)
Since AC is a radius, AC = 24.
This means that the area of ABC is 1/12 of the circle's area, and the length of arc BC is 1/12 of the circumference of the circle.
Since arc BC = \(4\pi\), the total circumference must be \(12(4\pi) = 48\pi\).
The circumference is equal to \(2\pi r\), where r is the radius. So:
\(2\pi r = 48\pi\)
Divide by \(2\pi\):
\(r = 24\)
Since AC is a radius, AC = 24.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the figure below, ABC is a circular sector with center A.
[#permalink]
01 Apr 2020, 08:00
01 Apr 2020, 08:00
1
Carcass wrote:
In the figure below, ABC is a circular sector with center A. If arc BC has length \(4\pi\), what is the length of AC?
Attachment:
#GREpracticequestion In the figure below, ABC is a circular .jpg
Show: :: OA
24
Here's the formula for finding the length of an arc:
GIVEN: arc BC has length \(4\pi\)
So, we can write: \((\frac{30}{360})(2\pi r) = 4\pi\)
Simplify the fraction: \((\frac{1}{12})(2\pi r) = 4\pi\)
Multiply both sides by \(12\) to get: \(2\pi r = 48\pi\)
Divide both sides by \(2\pi \) to get: \(r = 24\)
Since \(AC\) = the radius of the circle, we can see that \(AC = 24\)
Answer: 24
Cheers,
Brent
