The probability of the grain of sand landing on the portion of the base outside the triangle is 3/4. Hence, The probability of the grain of sand landing on the portion of the base inside the triangle is (1 - 3/4) = 1/4.
Therefore, the ratio of area of the triangle to the area of the base of the cylinder = 1/4
Say, length of each side of the equilateral triangle is a.
Hence, area of the equilateral triangle = (√3/4)*a²
Now, circumference of the base = 4√(π√3)
So, the radius of the base = 4√(π√3)/(2π)
So, area of the base = π[4√(π√3)/(2π)]² = π[16*(π√3)/(4π²)] = 4√3
Hence, area of the equilateral triangle = √3
Hence, (√3/4)*a² = √3 ---> a = √4 = 2
The correct answer is E.
Cylindrical tank
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
GMAT/MBA Expert
-
Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
-
coolhabhi
- Master | Next Rank: 500 Posts
- Posts: 141
- Joined: Tue Oct 04, 2011 5:17 am
- Thanked: 25 times
This problem feels to be very difficult but if read patiently then it is very easy. Here is what I did:
Given circumference 4√[�√3]
we know 2�r = 4√[�√3]
=> r = 2√[(√3)/�]
so Area of the base = �r^2 => � * (4√3)/�
Area of the base = 4√3
the problem says that the sand grain has a probability of falling outside the EQUILATERAL triangle is 3/4.
This means the area of the triangle is 1/4 of the total area of the base.
so area of the equilateral triangle is √3
But we know the area of the equilateral triangle is (√3/4)a^2
so (√3/4)a^2 = √3
a^2 = 4
a = 2
Answer is E
Given circumference 4√[�√3]
we know 2�r = 4√[�√3]
=> r = 2√[(√3)/�]
so Area of the base = �r^2 => � * (4√3)/�
Area of the base = 4√3
the problem says that the sand grain has a probability of falling outside the EQUILATERAL triangle is 3/4.
This means the area of the triangle is 1/4 of the total area of the base.
so area of the equilateral triangle is √3
But we know the area of the equilateral triangle is (√3/4)a^2
so (√3/4)a^2 = √3
a^2 = 4
a = 2
Answer is E
