The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindricalcanister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has maximum volume?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
I am not able to understand why cant we take 10 as the length so that radius becomes 5 and height is 8. giving us the maximum volume?
Geometry | OG 12
This topic has expert replies
- [email protected]
- Master | Next Rank: 500 Posts
- Posts: 206
- Joined: Sun Jun 24, 2012 5:44 pm
- Thanked: 5 times
- Followed by:3 members
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
Volume of cylinder = (pi) * radius² * height of cylinder[email protected] wrote:The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindricalcanister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has maximum volume?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
I am not able to understand why cant we take 10 as the length so that radius becomes 5 and height is 8. giving us the maximum volume?
If the cylinder is placed on 6 in by 8 in. face, then it's maximum radius is 6/2 = 3 and volume will be (pi) * 3² * 10 = 90(pi)
If the cylinder is placed on 6 in by 10 in. face, then it's maximum radius is 6/2 = 3 and volume will be (pi) * 3² * 8 = 72(pi)
If the cylinder is placed on 8 in by 10 in. face, then it's maximum radius is 8/2 = 4 and volume will be (pi) * 4² * 6 = 96(pi)
We can see that the volume is maximum when radius = 4 in.
The correct answer is B.
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/