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# A certain rectangular crate measures 8 feet by 10 feet by 12

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A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]  26 Dec 2004, 15:08
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A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?

A. 4
B. 5
C. 6
D. 8
E. 10

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-rectangular-crate-measures-8-feet-by-10-feet-by-100223.html
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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]  26 Dec 2004, 20:54
Ans is "B".

For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. So to maximize the above eqn, let's say base of crate is 10x12 that means vol is 200pi and if base is 8X10 vol is 192pi and with base of 8x12 it is 160pi. Therefore for max vol base should be 10x12 i.e. of radius 10/2 = 5
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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]  26 Dec 2004, 22:12
V=PI R2H
V=PI(5)2 (8)=200 PI

THEREFORE, R=5.

NOTE: R CANNOT BE 6. TO HAVE R=6, THE BASE OF THE CRATE MUST HAVE DIMENSIONS OF 12X12 OR MORE.

Last edited by MA on 28 Dec 2004, 21:51, edited 2 times in total.
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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]  28 Dec 2004, 21:58
kdhong wrote:
MA wrote:
V=PI R2H
V=PI(5)2 (8)=200 PI

THEREFORE, R=5.

NOTE: R CANNOT BE 6. TO HAVE R=6, THE BASE OF THE CRATE MUST HAVE DIMENSIONS OF 6X6 OR MORE.

How did you know that the height was 8?

because you are maximizing the volume of the tank. if you built the crate with the dimensions, r=5 and hight =8, then only you can have the largest volume of the cylinder.

Last edited by MA on 29 Dec 2004, 22:18, edited 1 time in total.
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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]  29 Dec 2004, 13:00
Okay i can't seem to understand the rationale here. Can someone pls explain better. Like pls break this down? Thanks
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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]  22 Jun 2014, 11:55
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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]  22 Jun 2014, 12:00
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kdhong wrote:
A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?

A. 4
B. 5
C. 6
D. 8
E. 10

Volume of the cylinder equals to $$area=\pi{r^2}h$$. First of all note that answer choices C, D, and E don't make sense. For example cylinder of a radius 6 (option C) just won't fit on any face, as max face has a dimensions 12*10 so cylinder with max radius of 5 can be placed on it.

Max volume will be when the base of a cylinder is placed on the face with dimension 12*10 thus the radius will be 5 --> $$v=\pi{5^2}*8=200\pi$$;

Other options:
If we place cylinder on the face with dimension 12*8 then radius will be 4 and $$v=\pi{4^2}*10=160\pi$$;
If we place cylinder on the face with dimension 10*8 then radius will be 4 and $$v=\pi{4^2}*12=192\pi$$,.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-rectangular-crate-measures-8-feet-by-10-feet-by-100223.html
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Re: A certain rectangular crate measures 8 feet by 10 feet by 12   [#permalink] 22 Jun 2014, 12:00
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