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

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Math Expert
Joined: 02 Sep 2009
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A right cone is to be placed within a rectangular box so that the cone  [#permalink]

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12 Nov 2019, 01:04
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Difficulty:

65% (hard)

Question Stats:

46% (01:39) correct 54% (01:44) wrong based on 96 sessions

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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. $$4π$$

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]

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Updated on: 12 Nov 2019, 12:37
1
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, 02:26.
Last edited by Archit3110 on 12 Nov 2019, 12:37, edited 1 time in total.
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Joined: 19 Oct 2018
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A right cone is to be placed within a rectangular box so that the cone  [#permalink]

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Updated on: 12 Nov 2019, 12:29
The maximum possible diameter of cone that can fit in the box, d= max{min(2,4), min(2,4), min(2,2)}=2

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, 12:18.
Last edited by nick1816 on 12 Nov 2019, 12:29, edited 1 time in total.
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Re: A right cone is to be placed within a rectangular box so that the cone  [#permalink]

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12 Nov 2019, 12:25
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

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

Posted from my mobile device
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Joined: 19 Oct 2018
Posts: 1985
Location: India
A right cone is to be placed within a rectangular box so that the cone  [#permalink]

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12 Nov 2019, 12:28
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

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

Posted from my mobile device
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Joined: 31 Oct 2015
Posts: 95
A right cone is to be placed within a rectangular box so that the cone  [#permalink]

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14 Nov 2019, 22:34
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 = $$\frac{1}{3}*\pi*1*4$$ = $$\frac{4}{3}*\pi$$

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Re: A right cone is to be placed within a rectangular box so that the cone  [#permalink]

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30 May 2020, 05:46
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]

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30 May 2020, 18:00
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?
Re: A right cone is to be placed within a rectangular box so that the cone   [#permalink] 30 May 2020, 18:00