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A right cone is to be placed within a rectangular box so that the cone

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Bunuel
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A right cone is to be placed within a rectangular box so that the cone [#permalink] New post   12 Nov 2019, 02:04
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A right cone is to be placed within a rectangular box so that the cone stands upright when the box is placed on one of its sides. If the dimensions of the box are 2 inches by 2 inches by 4 inches, then what is the greatest possible volume of such a cone?


A. \((\frac{2}{3})π\)

B. \((\frac{4}{3})π\)

C. \(2π\)

D. \((\frac{8}{3})π\)

E. \(4π\)


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Archit3110
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A right cone is to be placed within a rectangular box so that the cone [#permalink] New post   Updated on: 12 Nov 2019, 13:37
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vol of cone ; 1/3 * pi * r^2 *h
r has to be max to get max vol ; let side of base = 2 ; r = 1
h = 4
we get vol=
\((\frac{4}{3})π\)
IMO B

Bunuel wrote:
A right cone is to be placed within a rectangular box so that the cone stands upright when the box is placed on one of its sides. If the dimensions of the box are 2 inches by 2 inches by 4 inches, then what is the greatest possible volume of such a cone?


A. \((\frac{2}{3})π\)

B. \((\frac{4}{3})π\)

C. \(2π\)

D. \((\frac{8}{3})π\)

E. \(4π\)


Are You Up For the Challenge: 700 Level Questions

Originally posted by Archit3110 on 12 Nov 2019, 03:26.
Last edited by Archit3110 on 12 Nov 2019, 13:37, edited 1 time in total.
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nick1816
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A right cone is to be placed within a rectangular box so that the cone [#permalink] New post   Updated on: 12 Nov 2019, 13:29
The maximum possible diameter of cone that can fit in the box, d= max{min(2,4), min(2,4), min(2,2)}=2
radius, r= 1 inches

height, h= 4 inches

Volume= \(\frac{1}{3}* pi* r^2*h\)= \(\frac{1}{3}*pi*1^2*4\)= \(\frac{4}{3} pi\)


Bunuel wrote:
A right cone is to be placed within a rectangular box so that the cone stands upright when the box is placed on one of its sides. If the dimensions of the box are 2 inches by 2 inches by 4 inches, then what is the greatest possible volume of such a cone?


A. \((\frac{2}{3})π\)

B. \((\frac{4}{3})π\)

C. \(2π\)

D. \((\frac{8}{3})π\)

E. \(4π\)


Are You Up For the Challenge: 700 Level Questions

Originally posted by nick1816 on 12 Nov 2019, 13:18.
Last edited by nick1816 on 12 Nov 2019, 13:29, edited 1 time in total.
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Archit3110
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Re: A right cone is to be placed within a rectangular box so that the cone [#permalink] New post   12 Nov 2019, 13:25
nick1816 for box of 2x2x4 dimension how can a cone fit with height 4 and radius 2 ?
If one side is taken as 2 then won't it's radius be 1 ?

nick1816 wrote:
The maximum possible diameter of cone that can fit in the box, d= max{min(2,4), min(2,4), min(2,2)}=2
radius, r= 2 inches

height, h= 4 inches

Volume= \(\frac{1}{3}* pi* r^2*h\)= \(\frac{1}{3}*pi*1^2*4\)= \(\frac{4}{3} pi\)


Bunuel wrote:
A right cone is to be placed within a rectangular box so that the cone stands upright when the box is placed on one of its sides. If the dimensions of the box are 2 inches by 2 inches by 4 inches, then what is the greatest possible volume of such a cone?


A. \((\frac{2}{3})π\)

B. \((\frac{4}{3})π\)

C. \(2π\)

D. \((\frac{8}{3})π\)

E. \(4π\)


Are You Up For the Challenge: 700 Level Questions


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nick1816
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A right cone is to be placed within a rectangular box so that the cone [#permalink] New post   12 Nov 2019, 13:28
brother that was a typo... check i took 1 in the calculation. it happens when you post solutions at 2AM.


Archit3110 wrote:
nick1816 for box of 2x2x4 dimension how can a cone fit with height 4 and radius 2 ?
If one side is taken as 2 then won't it's radius be 1 ?

nick1816 wrote:
The maximum possible diameter of cone that can fit in the box, d= max{min(2,4), min(2,4), min(2,2)}=2
radius, r= 2 inches

height, h= 4 inches

Volume= \(\frac{1}{3}* pi* r^2*h\)= \(\frac{1}{3}*pi*1^2*4\)= \(\frac{4}{3} pi\)


Bunuel wrote:
A right cone is to be placed within a rectangular box so that the cone stands upright when the box is placed on one of its sides. If the dimensions of the box are 2 inches by 2 inches by 4 inches, then what is the greatest possible volume of such a cone?


A. \((\frac{2}{3})π\)

B. \((\frac{4}{3})π\)

C. \(2π\)

D. \((\frac{8}{3})π\)

E. \(4π\)


Are You Up For the Challenge: 700 Level Questions


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A right cone is to be placed within a rectangular box so that the cone [#permalink] New post   14 Nov 2019, 23:34
Volume of a cone is \(\frac{1}{3}*\pi*r^2*h\)

h=4 then r=1 ( we need a square base to fit the largest cone diameter)

There fore the largest volume is = \(\frac{1}{3}*\pi*1*4\) = \(\frac{4}{3}*\pi\)

The answer is B
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Re: A right cone is to be placed within a rectangular box so that the cone [#permalink] New post   30 May 2020, 06:46
I am not probably getting the diagram right in my head on this. Why can't the diameter be taken as 4 and height 2?
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Re: A right cone is to be placed within a rectangular box so that the cone [#permalink] New post   30 May 2020, 19:00
You can't fit a circle of diameter 4 cm in any of the faces of rectangular box

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Vniks wrote:
I am not probably getting the diagram right in my head on this. Why can't the diameter be taken as 4 and height 2?
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Re: A right cone is to be placed within a rectangular box so that the cone [#permalink] New post   07 Jan 2023, 13:15
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