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# A crate measures 4 feet by 8 feet by 12 feet on the inside...

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Manager
Joined: 04 Jun 2015
Posts: 85
A crate measures 4 feet by 8 feet by 12 feet on the inside...  [#permalink]

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20 Dec 2015, 09:21
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Difficulty:

65% (hard)

Question Stats:

57% (01:22) correct 43% (01:08) wrong based on 170 sessions

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A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?

A. 2
B. 4
C. 6
D. 8
E. 12

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Joined: 17 Dec 2015
Posts: 1
Re: A crate measures 4 feet by 8 feet by 12 feet on the inside...  [#permalink]

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20 Dec 2015, 22:06
1
A crate that is 4 by 8 by 12 has 3 faces.

Face 1: L=4, B=8, H=12. In trying to fit a circle into a 4 by 8 rectangle, diameter can only be maximized to be 4. As such, the volume of the cylinder is
pi X (4/2)^2 X 12 = 48pi

Face 2: L=4, B=12, H=8. Same as above, the circle has to fit into a 4 by 12 rectangle, diameter is 4. Volume of cylinder is
pi X (4/2)^2 X 8 = 32pi

Face 3: L=8, B=12, H=4. Lastly, the circle has to fit into a 8 by 12 rectangle, diameter is 8. Volume of cylinder is
pi X (8/2)^2 X 4 = 64pi

The volume in the 3rd scenario is the largest. As such, to maximize the volume of the cylinder, the radius has to be 8/2=4.
Intern
Joined: 12 Nov 2015
Posts: 48
Re: A crate measures 4 feet by 8 feet by 12 feet on the inside...  [#permalink]

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20 Dec 2015, 22:33
1
Sash143 wrote:
A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?

A. 2
B. 4
C. 6
D. 8
E. 12

We can find the radius of all the three cases of cylinders.

The only crux to find the answer faster is that:
Voulme is pi*r^2*h. The volume is a function of r^2. so r has to be the highest to find the largest volume.

So r=4 for the surface 8*12 face.

Volume = 64pi
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Joined: 04 Jun 2016
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A crate measures 4 feet by 8 feet by 12 feet on the inside...  [#permalink]

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17 Jul 2016, 03:15
1
Sash143 wrote:
A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?

A. 2
B. 4
C. 6
D. 8
E. 12

Just glancing at the dimensions of the crate makes us realise that it is a cuboid.

To fit the cylinder with largest radius inside this cuboig , we should make the base of the crate as wide as possible
so we will take the base as 12 feet by 8 feet
Now since the limiting number in the base is 8 feet; therefore a cylinder {we can visualise that a cylinder's width is its diameter } can only fit inside the crate if it is 8 feet or less.
Therefore the radius of the cylinder will become$$\frac{Diameter}{2}===> \frac{8}{2} = 4$$
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Manager
Joined: 23 Sep 2016
Posts: 95
A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone  [#permalink]

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03 Nov 2016, 10:19
A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?

A) 2
B) 4
C) 6
D) 8
E) 12
Math Expert
Joined: 02 Sep 2009
Posts: 48037
Re: A crate measures 4 feet by 8 feet by 12 feet on the inside...  [#permalink]

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03 Nov 2016, 10:57
SW4 wrote:
A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?

A) 2
B) 4
C) 6
D) 8
E) 12

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Re: A crate measures 4 feet by 8 feet by 12 feet on the inside...  [#permalink]

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12 Nov 2016, 00:46
3
Sash143 wrote:
A crate measures 4 feet by 8 feet by 12 feet on the inside. A stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides. What is the radius, in feet, of the pillar with the largest volume that could still fit in the crate?

A. 2
B. 4
C. 6
D. 8
E. 12

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Re: A crate measures 4 feet by 8 feet by 12 feet on the inside...  [#permalink]

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15 Sep 2017, 11:17
If the diameter is 4 then vol is 4x8pie
if diameter is 8 => vol = 16x4
diameter 12 not possible => diameter = 8 = radius 4 OPTION B
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Re: A crate measures 4 feet by 8 feet by 12 feet on the inside... &nbs [#permalink] 15 Sep 2017, 11:17
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