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Cylindrical tennis-ball cans are being packed into cartons. [#permalink]
 03 Dec 2007, 09:01
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Question Stats:
66% (02:08) correct
33% (01:36) wrong based on 3 sessions
Cylindrical tennis-ball cans are being packed into cartons. If each can has a radius of 2 inches and a height of 12 inches, and the dimensions of each carton are 14 inches by 16 inches by 20 inches, what is the maximum number of tennis-ball cans that can fit in each carton? A. 12 B. 15 C. 20 D. 24 E. 40
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C.
((14-2)/12)*(16/4)*(20/4)=20
Cylindrical tennis-ball can has 4*4*12 size
for 14 size of carton: 14=12+2(empty), 4*3+2(empty)
for 16 size of carton: 16=12+4(empty), 4*4+0(empty)
for 20 size of carton: 20=12+8(empty), 4*5+0(empty)
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Re: PS: Volume of cylinder and a box [#permalink]
04 Dec 2007, 23:29
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tarek99 wrote: Cylindrical tennis-ball cans are being packed into cartons. If each can has a radius of 2 inches and a height of 12 inches, and the dimensions of each carton are 14 inches by 16 inches by 20 inches, what is the maximum number of tennis-ball cans that can fit in each carton?
a) 12
b) 15
c) 20
d) 24
e) 40
I tried solving this by dividing the volume of this box by the volume of this cylinder, however, it didn't work cause i got roughly 30, while the OA is C. Can anyone show me how? would really appreciate it!
Diameter of can = 4
We can fill max. cans when the height is 14 and the base is 20 by 16.
This is because:
if base is 14 by 16 then we can fit a max of 14/4 * 16/4 = 12 cans.
if base is 14 by 20 then we can fit a max of 14/4 * 20/4 = 15 cans.
if base is 20 by 16 or 16 by 20 then we can fit a max of 20/4 * 16/4 = 20 cans.
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Re: PS: Volume of cylinder and a box [#permalink]
05 Dec 2007, 01:06
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tarek99 wrote: Cylindrical tennis-ball cans are being packed into cartons. If each can has a radius of 2 inches and a height of 12 inches, and the dimensions of each carton are 14 inches by 16 inches by 20 inches, what is the maximum number of tennis-ball cans that can fit in each carton?
a) 12
b) 15
c) 20
d) 24
e) 40
I tried solving this by dividing the volume of this box by the volume of this cylinder, however, it didn't work cause i got roughly 30, while the OA is C. Can anyone show me how? would really appreciate it!
Never try doing these by solving for volume, it doesnt really work that way. Heres why.
We want the most cans so want to fit as many cans in the length and width as possible.
So we have 16x20 which are both divisible by 4. (diameter of the can is 4).
so we can have 4 one way and 5 another so 20 total.
And 12 inches is the height of each can so they all fit.
C.
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thanks a lot guys. all of you gave valuable explanations. OA is C
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Re: PS: Volume of cylinder and a box [#permalink]
07 Jan 2011, 17:30
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Hi all. Was just going through the question. The answer would change if some cans are placed vertically and some horizontally.!!
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Re: PS: Volume of cylinder and a box [#permalink]
15 Jun 2011, 05:01
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i drew a table: hope its correct:
14 16 20
1 4 5
3 4 1
3 1 5
the height will fit only 1 time in every dimension (12 apears only once in 14/16/20) and the 4=d will apear 3 times in 14 and 4 times in 16 and 5 times in 20
hence 4*5
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Re: Cylindrical tennis-ball cans are being packed into cartons. [#permalink]
26 Aug 2012, 23:45
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Experts, one clarification - If I modify the question little bit and let the new dimensions be 16* 20 * 16 then we can obviously place 20 cylinders as above on the 16*20 base. Now, there will be 4 inches left in the height of the cuboid and we can place more cylinders in horizontal position over the vertical ones.Please clarify that shall we consider these extra ones - y/n
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http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
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Re: Cylindrical tennis-ball cans are being packed into cartons. [#permalink]
27 Aug 2012, 11:56
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+1 C You have to find the side of the box with the biggest area. In that side you will place the bottoms of the cans.
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Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
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Re: Cylindrical tennis-ball cans are being packed into cartons. [#permalink]
27 Aug 2012, 12:00
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catfreak wrote: Experts, one clarification - If I modify the question little bit and let the new dimensions be 16* 20 * 16
then we can obviously place 20 cylinders as above on the 16*20 base.
Now, there will be 4 inches left in the height of the cuboid and we can place more cylinders in horizontal position over the vertical ones.
Please clarify that shall we consider these extra ones - y/n I agree with you. There will be room for 6 cans I think. However, you have to consider that there are some industrial and safety restrictions 
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Re: Cylindrical tennis-ball cans are being packed into cartons.
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27 Aug 2012, 12:00
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