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.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
A sector has an arc length of 4π and a radius of 3. What is the centra
[#permalink]
04 Mar 2021, 06:00
04 Mar 2021, 06:00
Expert Reply
00:00
Question Stats:
80% (00:57) correct
20% (01:31) wrong based on 5 sessions
Hide Show timer Statistics
A sector has an arc length of 4π and a radius of 3. What is the central angle of the sector?
A. 60°
B. 90°
C. 180°
D. 240°
E. 270°
A. 60°
B. 90°
C. 180°
D. 240°
E. 270°
Re: A sector has an arc length of 4π and a radius of 3. What is the centra
[#permalink]
04 Mar 2021, 07:12
04 Mar 2021, 07:12
You can easily calculate the using the formula of arc length = (center angle / 360) * 2 * π * r
but, there is a more easy approach. Let's calculate the circumference first = 2 * π * r = 6 * π and the arc length is 4 * π
So, 6 * π will create an angle of 360° with the center cause it's covering the whole circle.
As, 4 * π is 2/3 of 6 * π the certer angle will be = 360° * (2 / 3) = 240°
Answer choice - D
but, there is a more easy approach. Let's calculate the circumference first = 2 * π * r = 6 * π and the arc length is 4 * π
So, 6 * π will create an angle of 360° with the center cause it's covering the whole circle.
As, 4 * π is 2/3 of 6 * π the certer angle will be = 360° * (2 / 3) = 240°
Answer choice - D
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: A sector has an arc length of 4π and a radius of 3. What is the centra
[#permalink]
04 Mar 2021, 07:36
04 Mar 2021, 07:36
1
GeminiHeat wrote:
A sector has an arc length of 4π and a radius of 3. What is the central angle of the sector?
A. 60°
B. 90°
C. 180°
D. 240°
E. 270°
A. 60°
B. 90°
C. 180°
D. 240°
E. 270°
Arc length \(= \frac{θ}{360}(2πr) = 4π\)
i.e. \(\frac{θ}{360}(3) = 2\)
\(\frac{θ}{120} = 2\)
\(θ = 240\)
Hence, option D
