Forum Home > GMAT > Quantitative > Problem Solving (PS)
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.
Aug 2211:00 AM EDT
-11:59 PM EDT
More and more TTP students are earning impressive scores on the GMAT. Now is the perfect time to join the many GMAT students who made the switch to TTP and surpassed their wildest expectations on test day.
Aug 2910:00 PM IST
-11:30 PM IST
With brand new features like:AI-driven Planner tool, 850+ data Insights practice questions and GMAT Focus Edition Adaptive mock tests with ESR+ analysis and personal mentor support, our course is the most comprehensive course for GMAT Focus Edition.
Aug 3112:00 PM EDT
-03:00 PM EDT
Save 20% on Target Test Prep and Score in the 100th Percentile in GMAT Verbal! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
Aug 3103:00 PM EDT
-11:59 PM EDT
For a limited time use code FALL20 to save on prep. Valid on Complete Course, Advanced Course, Bootcamp Course, Tutoring, and the Executive Assessment Course. This discount ends September 16th.
Sep 0212:01 AM PDT
-11:59 PM PDT
On Monday the 2nd, GMAT Club Tests will be Absolutely Free! Including all the Quizzes, Questions, and Tests. 12 AM - 11:59 PM PST- Sep 07
11:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
A is the center of the top face of the right circular cylinder in the
[#permalink]
10 Dec 2020, 01:15
10 Dec 2020, 01:15
4
Bookmarks
Expert Reply
Show timer
00:00
A
B
C
D
E
Difficulty:
55%
(hard)
Question Stats:
61% (02:29) correct
39%
(03:02)
wrong
based on 67
sessions
A is the center of the top face of the right circular cylinder in the figure above. If the degree measure of \(∠BAC\) is four times that of \(∠ACB\), and the height of the cylinder is equal to the diameter of its base, then the volume of the shaded region is what fraction of the volume of the entire cylinder?
A. 1/7
B. 1/6
C. 1/5
D. 1/4
E. 1/3
Attachment:
1.jpg [ 22.98 KiB | Viewed 3010 times ]
Re: A is the center of the top face of the right circular cylinder in the
[#permalink]
10 Dec 2020, 03:03
10 Dec 2020, 03:03
5
Kudos
My approach-
AC = AB radius, therefore angle ABC = angle ACB
if angle abc = x
then angle acb = x, angle bac = 4x
therefore x = 30 degrees (sum of all the angles is 180)
angle bac = 120
Volume proportion of shaded region to entire Cylinder= 120/360 =1/3
Kudos please, have to reach 25 for next level
AC = AB radius, therefore angle ABC = angle ACB
if angle abc = x
then angle acb = x, angle bac = 4x
therefore x = 30 degrees (sum of all the angles is 180)
angle bac = 120
Volume proportion of shaded region to entire Cylinder= 120/360 =1/3
Kudos please, have to reach 25 for next level
General Discussion
Re: A is the center of the top face of the right circular cylinder in the
[#permalink]
10 Dec 2020, 20:55
10 Dec 2020, 20:55
1
Kudos
A is the center of the top face of the right circular cylinder in the figure above. If the degree measure of \(∠BAC\) is four times that of \(∠ACB\), and the height of the cylinder is equal to the diameter of its base, then the volume of the shaded region is what fraction of the volume of the entire cylinder?
A. 1/7
B. 1/6
C. 1/5
D. 1/4
E. 1/3
AB=AC, Angle C= Angle B=x, Angle A=4x so in triangle ABC, x+x+4x=180 => x=30.
Angle A= 120,
Volume of Triangular portion/Volume of cylinder =120/360= 1/3
Answer E.
