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 length of arc PQR
[#permalink]
21 Dec 2022, 02:01
21 Dec 2022, 02:01
Expert Reply
1
Bookmarks
00:00
Question Stats:
39% (01:24) correct
60% (01:07) wrong based on 48 sessions
Hide Show timer Statistics
Attachment:
GRE The length of arc PQR.jpg [ 26.3 KiB | Viewed 3273 times ]
Point O is the center of the circle.
Quantity A |
Quantity B |
The length of arc PQR |
\(3\pi\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: The length of arc PQR
[#permalink]
23 Dec 2022, 05:00
23 Dec 2022, 05:00
Expert Reply
One side of the triangle oR is labeled as 2. Therefore, the \(C=2 \pi 2=4 \pi\)
If the angle is 60° that means the area of the circle OUTSIDE of the triangle is 5/6 of C
\(\frac{5}{6} * 4 \pi\)
\(\frac{20}{6} \pi = \frac{10}{3} \pi \)
\(\frac{10}{3} \pi > 3 \pi\)
If the angle is 60° that means the area of the circle OUTSIDE of the triangle is 5/6 of C
\(\frac{5}{6} * 4 \pi\)
\(\frac{20}{6} \pi = \frac{10}{3} \pi \)
\(\frac{10}{3} \pi > 3 \pi\)
The length of arc PQR
[#permalink]
30 Jan 2024, 20:07
30 Jan 2024, 20:07
1
\(\dfrac{Length of Arc PR}{Circumference of the Circle} = \dfrac{Angle of Arc}{Angle of Circumference} = \dfrac{60}{360} = \dfrac{1}{6}\)
The Length of Arc PR is \(\dfrac{1}{6}^{th}\) of Circumference of Circle
The Length of Arc PQR = \(1-\dfrac{1}{6} = \dfrac{5}{6}^{th}\) of Circumference of Circle
Since Circumference of the Circle is \(2 \pi r\)
Length of Arc PQR \(= 2 \pi r \times \dfrac{5}{6} = \dfrac{5 \pi r}{3}\)
Since \(r=2\) (given)
Length of Arc PQR \(= \dfrac{5 \pi 2}{3} = \dfrac{10 \pi}{3}\)
Now
\(\dfrac{10 \pi}{3} > 3 \pi\)
\(3.333 \pi > 3 \pi\)
Quantity A is the greatest.
The Length of Arc PR is \(\dfrac{1}{6}^{th}\) of Circumference of Circle
The Length of Arc PQR = \(1-\dfrac{1}{6} = \dfrac{5}{6}^{th}\) of Circumference of Circle
Since Circumference of the Circle is \(2 \pi r\)
Length of Arc PQR \(= 2 \pi r \times \dfrac{5}{6} = \dfrac{5 \pi r}{3}\)
Since \(r=2\) (given)
Length of Arc PQR \(= \dfrac{5 \pi 2}{3} = \dfrac{10 \pi}{3}\)
Now
\(\dfrac{10 \pi}{3} > 3 \pi\)
\(3.333 \pi > 3 \pi\)
Quantity A is the greatest.
