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 shown has center $F$ and radius 6
[#permalink]
29 Aug 2025, 00:19
29 Aug 2025, 00:19
Expert Reply
00:00
Question Stats:
87% (01:19) correct
12% (05:39) wrong based on 8 sessions
Hide Show timer Statistics
Attachment:
GRE The circle shown has center $F$ and radius 6 .png [ 156.73 KiB | Viewed 532 times ]
The circle shown has center $F$ and radius 6 . If the measure of angle $\(E F G\)$ is $\(60^{\circ}\)$, what is the combined area of the shaded regions, rounded to the nearest integer?
A. \(\sqrt{2}\)
B. 36
C. 37
D. 38
E. 40
- Part of the project: PrepClub Daily GRE Quant Questions: Arithmetic, Algebra, Geometry & DA - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
- Also replying to the unanswered questions
The circle shown has center $F$ and radius 6
[#permalink]
31 Aug 2025, 08:40
31 Aug 2025, 08:40
Expert Reply
Given:
- Circle with center $F$ and radius $r=6$.
- Central angle $\(\angle E F G=60^{\circ}\)$.
- Two shaded sectors, each corresponding to the $\(60^{\circ}\)$ angle.
Step 1: Calculate the area of one sector with central angle $\(60^{\circ}\)$
Area of a sector is
$$
\(\text { Area of sector }=\frac{\theta}{360^{\circ}} \times \pi r^2\)
$$
With $\(\theta=60^{\circ}\)$ and $r=6$,
$$
\(=\frac{60}{360} \times \pi \times 6^2=\frac{1}{6} \times \pi \times 36=6 \pi\)
$$
Step 2: Total shaded area (two sectors)
Since there are two identical shaded sectors,
$$
\(\text { Total shaded area }=2 \times 6 \pi=12 \pi\)
$$
Step 3: Approximate value
$$
\(12 \pi \approx 12 \times 3.1416=37.699\)
$$
Rounded to the nearest integer:
38
Final Answer:
D. 38
- Circle with center $F$ and radius $r=6$.
- Central angle $\(\angle E F G=60^{\circ}\)$.
- Two shaded sectors, each corresponding to the $\(60^{\circ}\)$ angle.
Step 1: Calculate the area of one sector with central angle $\(60^{\circ}\)$
Area of a sector is
$$
\(\text { Area of sector }=\frac{\theta}{360^{\circ}} \times \pi r^2\)
$$
With $\(\theta=60^{\circ}\)$ and $r=6$,
$$
\(=\frac{60}{360} \times \pi \times 6^2=\frac{1}{6} \times \pi \times 36=6 \pi\)
$$
Step 2: Total shaded area (two sectors)
Since there are two identical shaded sectors,
$$
\(\text { Total shaded area }=2 \times 6 \pi=12 \pi\)
$$
Step 3: Approximate value
$$
\(12 \pi \approx 12 \times 3.1416=37.699\)
$$
Rounded to the nearest integer:
38
Final Answer:
D. 38
gmatclubot
The circle shown has center $F$ and radius 6 [#permalink]
31 Aug 2025, 08:40
Moderators:
