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# The inside dimensions of a rectangular wooden box are 6 inches by 8 in

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Intern
Joined: 02 Jan 2010
Posts: 5

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The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

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16 Jan 2010, 22:05
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Question Stats:

46% (01:13) correct 54% (01:21) wrong based on 61 sessions

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The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

[Reveal] Spoiler:
This is a very basic OG question.
The official answer is B because the cylinder of maximum volume that can be fit into the box will have to rest on the 8x10 face.

my query is
Quote:
A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces.

Does this not imply that the cylinder has to rest on one either the 6X10 or the 6x8 face.
And therefore cannot have a radius greater than 3.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-inside-d ... 28053.html
[Reveal] Spoiler: OA

Kudos [?]: 4 [0], given: 0

Senior Manager
Joined: 25 Jun 2009
Posts: 298

Kudos [?]: 150 [0], given: 6

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

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17 Jan 2010, 02:48
anil4410 wrote:
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. of all such canisters that could be used, What is the radius, in inches, of the one that has maximum volume?

a)3
b)4
c)5
d)6
e)8

This is a very basic OG question.
The official answer is B because the cylinder of maximum volume that can be fit into the box will have to rest on the 8x10 face.

my query is
Quote:
A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces.

Does this not imply that the cylinder has to rest on one either the 6X10 or the 6x8 face.
And therefore cannot have a radius greater than 3.

The question asks for cylindrical canister which has the maximum volume ( bigger the radius bigger the volume will be V = pi r^2h)

Radius will be maximum when we the area of the base of the cuboid is maximum, options are 6 x8 , 6 x10 and 8 x 10,

Out of these if we choose first 2 options maximum diameter for the cylinder would be 6 ( or Radius as 3),
Hence the last option 8 x10, so the diameter of the cylinder becomes 8 and radius 4

I hope this will help ..!

Cheers

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Manager
Joined: 26 Nov 2009
Posts: 162

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Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

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17 Jan 2010, 09:24
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KUDOS
to have the maximum radius we should rest the wooden box with max dimensions as base

for the wooden box 6*10*8 it should rest with 10*8 as base and 6 as height .

for the given dimension 10*8 the maximum possible radius will be 4 since if radius is greater than 4 than side with dimension 8 will not be able to accomadate it

so the ans is b)3

Kudos [?]: 62 [1], given: 5

Intern
Joined: 17 Jan 2016
Posts: 22

Kudos [?]: 9 [0], given: 249

Location: India
Concentration: General Management, General Management
Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

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02 Mar 2017, 01:28
There are 3 possible surfaces of this cuboid where the base of the cylinder will rest.They are

a) 6 X 8 - If the cylinder is placed in this position, it's dia would be the smallest of these two. Otherwise the cylinder cannot be accommodated. It's height would be 10 inches. So volume would be - 282.

b) 8 X 10 - Dia in this case would be 8 and height - 6. So volume would be - 301.

c) 10 X 6 - Dia in this case would be 6 and height - 8. So volume here would be - 226.

Clearly the the dia would be 8 and hence the radius should be 4 for the cylinder to have maximum volume.

Kudos [?]: 9 [0], given: 249

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129094 [0], given: 12194

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

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02 Mar 2017, 05:18
anil4410 wrote:
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

[Reveal] Spoiler:
This is a very basic OG question.
The official answer is B because the cylinder of maximum volume that can be fit into the box will have to rest on the 8x10 face.

my query is
Quote:
A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces.

Does this not imply that the cylinder has to rest on one either the 6X10 or the 6x8 face.
And therefore cannot have a radius greater than 3.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/the-inside-d ... 28053.html

$$volume_{cylinder}=\pi{r^2}h$$

If the cylinder is placed on 6*8 face then it's maximum radius is 6/2=3 and $$volume==\pi*{3^2}*10=90\pi$$;
If the cylinder is placed on 6*10 face then it's maximum radius is 6/2=3 and $$volume==\pi*{3^2}*8=72\pi$$;
If the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and $$volume==\pi*{4^2}*6=96\pi$$;

So, the maximum volume is for $$r=4$$.

Hope it's clear.

P.S. Notice that radii of 5, 6, and 8 (options C, D and E) are not possible.
_________________

Kudos [?]: 129094 [0], given: 12194

Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in   [#permalink] 02 Mar 2017, 05:18
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# The inside dimensions of a rectangular wooden box are 6 inches by 8 in

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