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

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Intern
Joined: 06 Aug 2007
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Here's one from OG... The inside dimensions of a rectangular [#permalink]  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?
VP
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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?
Intern
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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.
Intern
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jdel,

Why cant d be 10, so r=5? and we get the biggest volume?
Intern
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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?
Intern
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Yes Ofcourse! Something basic I overlooked
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