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Here's one from OG... The inside dimensions of a rectangular

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Here's one from OG... The inside dimensions of a rectangular [#permalink] New post 08 Aug 2007, 16:34
Here's one from OG...

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister 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 value?
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 [#permalink] New post 08 Aug 2007, 17:22
Imagine, rectangle of 10by8 and a circle inscribed. draw it yourself and see what can be the radius. it is half of 8 or 4
so i think it should be four,
it is difficult to explain but if you draw u will see the picture.

any ideas?
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 [#permalink] New post 08 Aug 2007, 18:31
there are three possible bottoms to the box

the 6*8 side on the the bottom, height 10- the biggest circle you could fit on this side has d=6, r=3, so volume is 9(pi)*10 or 90(pi).

6*10 side on bottom, height 8. d=6, r=3, volume, 9(pi)8 or 72(pi)

10*8 side on bottom, height 6. d=8, r=4, volume 16(pi)6 = 96(pi)

so r=4.
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 [#permalink] New post 08 Aug 2007, 19:26
jdel,

Why cant d be 10, so r=5? and we get the biggest volume?
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 [#permalink] New post 08 Aug 2007, 19:32
in order for a circle with radius 10 to fit into the rectangle, both sides of the rectangle have to be at least 10. another way to think about it -- imagine you have an 8x10 rectangle and you have a circle with diameter 8 in it. if that circle got any bigger (closer to ten) it would extend past the boundaries fo teh rectangle on the 8 inch side. this help?
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 [#permalink] New post 08 Aug 2007, 19:39
Yes Ofcourse! Something basic I overlooked :oops:
  [#permalink] 08 Aug 2007, 19:39
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Here's one from OG... The inside dimensions of a rectangular

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