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# Cylindrical tennis-ball cans are being packed into cartons.

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Intern
Joined: 14 Oct 2004
Posts: 27
Cylindrical tennis-ball cans are being packed into cartons. [#permalink]

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26 Nov 2004, 12:50
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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?
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Senior Manager
Joined: 19 Oct 2004
Posts: 315
Location: Missouri, USA

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26 Nov 2004, 14:02
Divide the volume of the box (l*b*h) by the volume of each can (pi*r^2*h)
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Manager
Joined: 18 Sep 2004
Posts: 64

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26 Nov 2004, 14:45
I got 20.

As the radius = 2 => Diameter = 4. So, we can think of the cylinders as boxes with dimension 4*4*12. So, on the surface area of 20*16, we can keep (20/4)*(16/4) = 20 cylinders. Cann't fit anything in rest of the volume left ((14-12)*16*20). So, final answer = 20.

Can anyone think of any easier way of doing it?

ruhi160184 - simply dividing the volumes may not work due to the shape of cyliner. When fit in a box some space will remain between 4 cyliners that cann't be filled.
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Thanks !

Aspire

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Joined: 19 Oct 2004
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Location: Missouri, USA

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26 Nov 2004, 14:53
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Manager
Joined: 18 Sep 2004
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26 Nov 2004, 15:14
ruhi160184 - Please see the attachment. I have tried to show the cross section of 4 cylinders. As the shaded portion will always remain empty, the circlular cross section of the cyliner with diameter = 4 is same as a box with a square cross section of 4*4.

Once you understand this point, we can rephrase the question as "how many boxes of dimension 4*4*12 can be fit into a box of dimension 16*20*14". Rest follows....

Hopefully it is clear now.
Attachments

Cylinder.doc [26.5 KiB]

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Aspire

Senior Manager
Joined: 19 Oct 2004
Posts: 315
Location: Missouri, USA

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26 Nov 2004, 15:21
HATS OFF TO YOU!! understood it now.
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Intern
Joined: 14 Oct 2004
Posts: 27

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26 Nov 2004, 16:57
OA is 20..Thanks for the explanation.
Manager
Joined: 30 Jul 2004
Posts: 101

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27 Nov 2004, 23:40
How come we came to 20 cylinders ?

I understood the shaded portion logic by aspire but could not understand how come you guys came to answer 20.

Because carton has dim. 14*16*20 and cyclindrical can now has dim as 4*4*12....
Manager
Joined: 18 Sep 2004
Posts: 64

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28 Nov 2004, 07:59
My approach =>

A surface area of 16*20 can have 20 squares of dimension 4*4 [calculation: (16*20)/(4*4) = 20].

As the height of cyliner is 12, we are left with 14-12=2. As the lowest side is 4, we cann't fit anything into a space of 2.

So, the final answer is 20.
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Thanks !

Aspire

28 Nov 2004, 07:59
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