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

Question

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

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

diaperman · Answer

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.

neha1993 · Answer

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

LogicGuru1 · Answer

Answer is B

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

SW4 · Answer

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

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

Bunuel · Answer

Please search before posting!

GMATinsight · Answer

Answer: Option B

Check the solution as attached

sahilvijay · Answer

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

warrior1991 · Answer

VeritasKarishma   chetan2u   Bunuel   gmatbusters

Please help.
Why cannot we take diameter as 12 in this case and mark 6 as radius??

GMATBusters · Answer

The diameter of 12 is not possible as the other dimensions are 4 and 8.
The  dia must be least of the sides of any face of the cuboid box , otherwise it will not fit in the box.
 Try to draw the circle of 12 dia in the rectangle 12*4 or 12*8, you will see that it will not be inside the rectangle.

bumpbot · Answer

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

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

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