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A rectangular steel container has three equal dimensions of

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A rectangular steel container has three equal dimensions of  [#permalink]

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New post 06 Dec 2010, 02:58
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C
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A rectangular steel container has three equal dimensions of 8 inches. If a cylindrical canister is to be placed inside the box so that it stands upright when the box rests on one of its six faces, what is the maximum possible volume, in cubic inches, of the canister?

(A) 128
(B) 64
(C) 128(3.14)
(D) 512
(E) 512(3.14)
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Re: Rectangular Solid  [#permalink]

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New post 06 Dec 2010, 03:14
surendar26 wrote:
A rectangular steel container has three equal dimensions of 8 inches. If a cylindrical canister is to be placed inside the box so that it stands upright when the box rests on one of its six faces, what is the maximum possible volume, in cubic inches, of the canister?
(A) 128
(B) 64
(C) 128(3.14)
(D) 512
(E) 512(3.14)


"A rectangular steel container has three equal dimensions of 8 inches" means that the container is a cube. Now, cylinder to have maximum possible volume it should have maximum possible diameter and height, so a diameter equal to a side of the cube, so d=8 (radius=4) and a height also equal to a side of the cube, so height=8: \(volume_{cylinder}=\pi{r^2}h=128\pi\).

Answer: C.
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Re: A rectangular steel container has three equal dimensions of  [#permalink]

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New post 02 Oct 2014, 01:54
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All dimensions are same of the rectangle, it means its a cube

The base would be a square

Maximum possible diameter of a inscribed circle (the cylinder) is the side of the square = 8

Radius = 4

Height = 8

\(Area = \pi r^2 h = \pi * 4^2 * 8 = 128\pi\)

Answer = C
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Re: A rectangular steel container has three equal dimensions of  [#permalink]

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Re: A rectangular steel container has three equal dimensions of   [#permalink] 25 Oct 2018, 10:17
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