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largest volume

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largest volume [#permalink]  07 Oct 2011, 10:54
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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
[Reveal] Spoiler: OA

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Re: largest volume [#permalink]  07 Oct 2011, 12:45
Hi,

This is my first post and response to any question in this forum.

Solution : To get the maximum base of the cylinder the crate has to be of dimension 10*12. Now the challenge is to identify what is lenght and what is width.

If 12 is the diameter of the cylinder then cylinder of equal proportion will not fit in one side of crate. So diameter has to be 10 so that cylinder will fit in the base of crate.

Radius will be 5 So answer is 5.

Thanks
Sourabh
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Re: largest volume [#permalink]  08 Oct 2011, 00:26
Vol= k*r^2*h

Dimensions are important to avoid confusion.
you can't have a 12*8 base as the circle won't fit in
so 10*12 is the best option
12 can't be an option for diameter.
so the diameter is 10
Hence radius is 5.
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Re: largest volume [#permalink]  09 Oct 2011, 20:53
Vol= k*r^2*h

Dimensions are important to avoid confusion.
you can't have a 12*8 base as the circle won't fit in
so 10*12 is the best option
12 can't be an option for diameter.
so the diameter is 10
Hence radius is 5.

Thre is a confusion here ..
i think in a 12*8 base circle will fit in if the radius is 4.
We cannot have 12 as diameter because it will not fit as other sides are smaller than this.
So it is between 12*10 and 12*8 with 10 and 8 diameters respectively.

but we need maximum volume so it should be 12*10 with 10 as diameter
ans r = 5
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Re: largest volume [#permalink]  11 Oct 2011, 23:01
Hey '

Can you explain why diameter of 12 is not workable ?
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Re: largest volume [#permalink]  12 Oct 2011, 01:59
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Priyanka2011 wrote:
Hey '

Can you explain why diameter of 12 is not workable ?

As per the question the cylinder should fit in the crate.

If The dimension of the base is l*b then the diameter of the circle should be equal or less than the smaller side.Otherwise the it will not fit in. it will look lik below image.

Here we have three options 12X10 or 12X8 or 10 X 8 of all these 12 X 10 will give the largest volume.
Attachments

2.JPG [ 8.93 KiB | Viewed 1306 times ]

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Re: largest volume [#permalink]  12 Oct 2011, 07:35
hey Gopu

Just didnt get the logic.. thanx a tonne +1 K
Senior Manager
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Re: largest volume [#permalink]  23 Oct 2011, 01:53
the area or volume are maximum when the dimensions are as close to each other as possible as is the case in square or cube. so, 12x10 would be the dimensions of the cylinder. a circle only fits perfectly inside of a square (inscribed) not a rectangle, so d=12 will not fit 12x10. therefore, d has to be 10, to fit inside 12x10, and h=12 to make the $$v=300\pi$$.
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Re: largest volume   [#permalink] 23 Oct 2011, 01:53
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