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The inside dimensions of a rectangular wooden box are 6

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The inside dimensions of a rectangular wooden box are 6 [#permalink] New post 05 Feb 2006, 05:44
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The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister 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 cannisters 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
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 [#permalink] New post 05 Feb 2006, 07:12
this problem is in the OG , and i never understood the OE they have given there... anybody pls help us! :shock:
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 [#permalink] New post 05 Feb 2006, 08:05
it should be 4 and not 5, if I understood the trick.
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 [#permalink] New post 05 Feb 2006, 09:21
thearch wrote:
it should be 4 and not 5, if I understood the trick.


can u share ur trick with me too! i never got the explanation for this right!
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 [#permalink] New post 05 Feb 2006, 09:45
razrulz wrote:
thearch wrote:
it should be 4 and not 5, if I understood the trick.


can u share ur trick with me too! i never got the explanation for this right!


well, provided that my answer is correct, the point made here is:
can you inscribe (I mean, perfectly) a circle in a rectangle? the asnwer is no

you can do that with squares, not with rectangles.

Since we're dealing with a rectangle, which is 10x8, we can't inscribe a circle of radius 5 in this rectangle. It wouldn't fit in the box.
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 [#permalink] New post 05 Feb 2006, 09:51
thearch wrote:
razrulz wrote:
thearch wrote:
it should be 4 and not 5, if I understood the trick.


can u share ur trick with me too! i never got the explanation for this right!


well, provided that my answer is correct, the point made here is:
can you inscribe (I mean, perfectly) a circle in a rectangle? the asnwer is no

you can do that with squares, not with rectangles.

Since we're dealing with a rectangle, which is 10x8, we can't inscribe a circle of radius 5 in this rectangle. It wouldn't fit in the box.


thnks a ton dear!!! how cld i ve missed it ? A cylinder is read.. and i overlooked it... :lol: thnks again
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 [#permalink] New post 05 Feb 2006, 10:02
thearch wrote:
razrulz wrote:
thearch wrote:
it should be 4 and not 5, if I understood the trick.


can u share ur trick with me too! i never got the explanation for this right!


well, provided that my answer is correct, the point made here is:
can you inscribe (I mean, perfectly) a circle in a rectangle? the asnwer is no

you can do that with squares, not with rectangles.

Since we're dealing with a rectangle, which is 10x8, we can't inscribe a circle of radius 5 in this rectangle. It wouldn't fit in the box.



Great stuff thearch! Got the same answer, but I like your diagramming skills. :cool
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 [#permalink] New post 05 Feb 2006, 11:28
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister 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 cannisters that could be used, what is the radius, in inches, of the one that has maximum volume?


Volueme is pir^2h

Now we can have three posibility of cylinder 6,8,10

h = 6 and r=min(8/2,10/2) = pi 4^2 6 = 96pi

h = 8 and r=min(6/2,10/2) = pi 3^2 8 = 72pi

h = 10 and r=min(6/2, 8/2) = pi 3^2 10 = 90pi

So r =4
  [#permalink] 05 Feb 2006, 11:28
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