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

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

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The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister 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 cannisters that could be used, what is the radius, in inches, of one that has the maximum volume?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
[Reveal] Spoiler: OA

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

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New post Updated on: 05 Dec 2017, 09:17
Bunuel wrote:
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister 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 cannisters that could be used, what is the radius, in inches, of one that has the maximum volume?

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


Let's assume that the bottom side of the box has dimensions 8*10 when the canister is placed in it. Obviously, the diameter can't be more than eight so the radius is 4 Height is 6
\(V = \pi * r^2 * h = 16\pi * 6 = 96\pi\)

Let's assume that the bottom side of the box has dimensions 8*6 when the canister is placed in it. Obviously, the diameter can't be more than 6 so the radius is 3 Height is 10
\(V = \pi * r^2 * h = 9\pi * 10 = 90\pi\)

B is the answer

Originally posted by Vorovski on 05 Dec 2017, 00:31.
Last edited by Vorovski on 05 Dec 2017, 09:17, edited 2 times in total.
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The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

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New post Updated on: 07 Dec 2017, 16:41
Bunuel wrote:
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister 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 cannisters that could be used, what is the radius, in inches, of one that has the maximum volume?

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


Volume of a cylinder: \(pi*r^2*h\)
Radius = \(\frac{Diameter}{2}\)

The maximum diameter of a cylinder that fits inside the rectangular box is restricted to the length and width of the box.
So, if we have a length =8, width = 10 and height = 6, then max. diameter = 8 and radius = 4;
And, the volume of the cylinder: \(pi*4^2*6=pi*96\)

Let's try another, with length =8, width = 6 and height = 10, then max. diameter = 6 and radius = 3;
And, the volume of the cylinder: \(pi*3^2*10=pi*90\)

Largest radius we can have is 4.
(B) is the answer.

Originally posted by exc4libur on 05 Dec 2017, 05:35.
Last edited by exc4libur on 07 Dec 2017, 16:41, edited 1 time in total.
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Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in [#permalink]

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New post 05 Dec 2017, 07:34
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exc4libur wrote:
Bunuel wrote:
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical cannister 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 cannisters that could be used, what is the radius, in inches, of one that has the maximum volume?

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


Volume of a cylinder: \(pi*r^2*h\)

Let's test the wooden box dimensions for the bottom and the height.
If we have a bottom of 6 and a height of 10 then the radius would be 3 and volume of cylinder = \(pi*3^2*10 = pi*90\)
If we have a bottom of 8 and a height of 10 then the radius would be 4 and volume of cylinder = \(pi*4^2*10 = pi*160\)
If we have a bottom of 10 and a height of 8 then the radius would be 5 and volume of cylinder = \(pi*5^2*8 = pi*200\)

So the maximum volume of the cylinder would be \(pi*200\) with a radius of 5.

(C) is the answer.


Might i check if you have considered how the cylinder could fit in?

For example, the length of the bottom is 10 and the height is 8, that means the width the bottom is 6. How do you fit in a cylinder with a radius of 5 (i.e., diameter = 10) while the width is only 6?

IMO the answer is B
Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in   [#permalink] 05 Dec 2017, 07:34
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The inside dimensions of a rectangular wooden box are 6 inches by 8 in

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