Events & Promotions
|
|
GMAT 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.
Apr 2212:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 1612:00 PM EDT
-11:59 PM EDT
You’re first to know: Save $200 on GMAT prep starting tomorrow, 4/13. Get 6 official practice tests and study with real questions. Be ready to save!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
06 Feb 2016, 17:17
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
88% (02:21) correct
13%
(02:06)
wrong
based on 32
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of the shaded portion in circle O, as pictured above, with m< O=60° and radius r = 10?
A) \(\frac{50}{3}\) \(\pi\) − \(50\sqrt{3}\)
B) \(\frac{50}{3}\) \(\pi\) − 50
C) \(\pi \sqrt{3}\)
D) \(\frac{50}{3}\) \(\pi\) − \(25\sqrt{3}\)
E) \(\frac{50}{3}\) \(\pi\)
A) \(\frac{50}{3}\) \(\pi\) − \(50\sqrt{3}\)
B) \(\frac{50}{3}\) \(\pi\) − 50
C) \(\pi \sqrt{3}\)
D) \(\frac{50}{3}\) \(\pi\) − \(25\sqrt{3}\)
E) \(\frac{50}{3}\) \(\pi\)
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
06 Feb 2016, 18:31
Kudos
Bookmarks
It is not a hard problem, if you know the Area of a circle segment and the value of sin for a 60 degree angle.
A=\(\frac{r^2}{2}\)*(\(\frac{\pi*\alpha}{180}\)-sin\(\alpha\))
Sin \(\alpha\) 60 = \(\frac{\sqrt{3}}{2}\)
Another way is to find the Area of the triangle and the Area of the sector of circle to find the Area of the Segment of the Circle.
Area Sector - Area Triangle = Area Segment.
Hope it helps.
Ans. D)
A=\(\frac{r^2}{2}\)*(\(\frac{\pi*\alpha}{180}\)-sin\(\alpha\))
Sin \(\alpha\) 60 = \(\frac{\sqrt{3}}{2}\)
Another way is to find the Area of the triangle and the Area of the sector of circle to find the Area of the Segment of the Circle.
Area Sector - Area Triangle = Area Segment.
Hope it helps.
Ans. D)
07 Feb 2016, 02:32
Kudos
Bookmarks
As mentioned by FelixM, you simply need to take the area of the sector/circle slice and subtract the area of the interior triangle.
Area of the circle slice:
1. \(\frac{60°}{360°} * π 10 ^2\)
2. (1) reduces into \(\frac{{π 50}}{3}\)
Area of the triangle:
1. We see that the interior angle of our triangle is 60°. We are dealing with an equilateral triangle.
2. We bisect our triangle down the middle to find our height. When we bisect the triangle, that creates two sub-triangles, mirrored, each conforming to the 30-60-90 special triangle. Plugging in the magic numbers for this triangle gives us a triangle height of \(5\sqrt{3}\).
3. \(5 \sqrt{3} * 10 * \frac{1}{2} = 25 \sqrt{3}\)
To find the area of the shaded portion:
1. As mentioned above, subtract the area of the triangle from the area of the sector: \(\frac{{π 50}}{3} - 25\sqrt{3}\), which is option D.
Area of the circle slice:
1. \(\frac{60°}{360°} * π 10 ^2\)
2. (1) reduces into \(\frac{{π 50}}{3}\)
Area of the triangle:
1. We see that the interior angle of our triangle is 60°. We are dealing with an equilateral triangle.
2. We bisect our triangle down the middle to find our height. When we bisect the triangle, that creates two sub-triangles, mirrored, each conforming to the 30-60-90 special triangle. Plugging in the magic numbers for this triangle gives us a triangle height of \(5\sqrt{3}\).
3. \(5 \sqrt{3} * 10 * \frac{1}{2} = 25 \sqrt{3}\)
To find the area of the shaded portion:
1. As mentioned above, subtract the area of the triangle from the area of the sector: \(\frac{{π 50}}{3} - 25\sqrt{3}\), which is option D.
