A rectangular box has the dimensions 12 inches x 10 inches x : Quant Question Archive [LOCKED]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 10:20

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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A rectangular box has the dimensions 12 inches x 10 inches x

Author Message
Manager
Joined: 19 Aug 2007
Posts: 169
Followers: 1

Kudos [?]: 51 [0], given: 0

A rectangular box has the dimensions 12 inches x 10 inches x [#permalink]

Show Tags

14 Oct 2007, 16:45
1
This post was
BOOKMARKED
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?

Answer: The radius of the cylinder must be equal to half of the smaller of the 2 dimensions that form the box's bottom. ............... and teh answer is 200 x pi

I just don't understand why does the radius half to be equal to half of the smaller of the 2 dimensions. does anyone understand why? thx.
Intern
Joined: 11 Nov 2006
Posts: 31
Followers: 0

Kudos [?]: 0 [0], given: 0

Show Tags

14 Oct 2007, 18:05
well, if the base of the cilinder stands lets say on the side 10 by 8, to make it fit in the rectangular box, radius of cilinder has to be 4, it won't just fit any other way. And if it stands on 12 by 10 side, radius has to be 5. Just try drawing it...
Intern
Joined: 14 Oct 2007
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Show Tags

14 Oct 2007, 20:40
There are 3 options here.

1) The height (H) of the cylinder is 12 so the Max diameter (D) it can have is 8. So the area (A)= 192

2) H = 8 and max. D = 10. So A = 200

3) H = 10 and max. D = 8. So A = 160.

Therefore the answer is 200 (pi)
CEO
Joined: 29 Mar 2007
Posts: 2583
Followers: 19

Kudos [?]: 421 [1] , given: 0

Show Tags

14 Oct 2007, 21:18
1
KUDOS
jimjohn wrote:
A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?

Answer: The radius of the cylinder must be equal to half of the smaller of the 2 dimensions that form the box's bottom. ............... and teh answer is 200 x pi

I just don't understand why does the radius half to be equal to half of the smaller of the 2 dimensions. does anyone understand why? thx.

Its helpful to draw this out.

1st Cyl. L,W,H : 12,10,8
Greatest diameter we can have is 10. (can't be 12 b/c it wouldnt fit in the box). So radius is equal to 5.

pir^2h = Vol of Cyl.

pi5^2*8 25*8=200.

2nd Cyl: L,W,H: 10,8,12

pi4^2*12 --> 16*12 =192

3rd Cyl: L,W,H: 8,10,12

No need to calculate as we can see this is going to be smaller than 2.

Dimensions L,W,H: 12,10,8 result in the greatest volume for a cylinder.

In answer to ur question. Draw a square, forget the cube.

Do dimensions 12 and 10. Now draw a line from the midpoint of one side of the square to another side of the square.

now draw a circle. you will see that only when the diameter is 10 will it actually fit in the box.
Director
Joined: 03 May 2007
Posts: 886
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 190 [0], given: 7

Show Tags

14 Oct 2007, 21:31
jimjohn wrote:
A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?

Answer: The radius of the cylinder must be equal to half of the smaller of the 2 dimensions that form the box's bottom. ............... and teh answer is 200 x pi

I just don't understand why does the radius half to be equal to half of the smaller of the 2 dimensions. does anyone understand why? thx.

the possible dimeters are either 10 or 8 but it cannot be 12. to have 12 as dimeter, we need another dimension at least of 12 or grater. so

1: if d = 10, then h = 8
so v = pi r^2 h = pi (5)^2 8 = 200 pi

2: if d = 8, h = 12
so v = pi r^2 h = pi (4)^2 12 = 192 pi

so first is the max.
Director
Joined: 22 Aug 2007
Posts: 567
Followers: 1

Kudos [?]: 50 [0], given: 0

Show Tags

18 Oct 2007, 20:37
jimjohn wrote:
A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?

Answer: The radius of the cylinder must be equal to half of the smaller of the 2 dimensions that form the box's bottom. ............... and teh answer is 200 x pi

I just don't understand why does the radius half to be equal to half of the smaller of the 2 dimensions. does anyone understand why? thx.

200pi is max volume.

The height of cylinder can be 12, 10 or 8

if height is 12, max diameter is 8----------> Volume is 12 x 16pi=192pi
if height is 10, max diameter is 8----------> Volume is 10 x 16pi=160pi
if height is 8, max diameter is 10---------->Volume is 16 x 10pi=200pi
Re: geometry question   [#permalink] 18 Oct 2007, 20:37
Display posts from previous: Sort by