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# Volume Cylinder

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23 Apr 2010, 06:29
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Q:A rectangular box has the dimensions 12 in x10in x8in. What is the largest possible volume of a right circular cylinder that is placed inside the box?

Can someone please provide detailed explanation for this problem?
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23 Apr 2010, 07:11
srichaks wrote:
Q:A rectangular box has the dimensions 12 in x10in x8in. What is the largest possible volume of a right circular cylinder that is placed inside the box?

Can someone please provide detailed explanation for this problem?

volume = pi*r^2*h
when radius is max then volume will be max
so in this we can have 10in as diameter so radius will be 5in.
then height will be 8in
so
vol = 200pi

what is the OA?
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23 Apr 2010, 07:53
IMO 360 Pi

Volume of cylinder = Pi * r^2 * h

this will be max when r = 12/2 = 6 and h = 5 ...since r is squared, maximum value of r should be taken.

volume = pi * 6^2 * 10 = 360 pi
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23 Apr 2010, 08:07
IMO 200pi.

As all the dimensions are different. So. the key here is to find the maximum radius the circular faces. In this case if the cylinder is placed in vertical position with height = 8 and radius = 10/2 then the area will be maximux = 200pi.

We cant take longest side as diameter because of different dimensions. So, 360pi is ruled out.

We cant take 8 in as the diameter, well in that case area = 192pi.
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23 Apr 2010, 08:09
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IMO 200pi.

As all the dimensions are different. So. the key here is to find the maximum radius the circular faces. In this case if the cylinder is placed in vertical position with height = 8 and radius = 10/2 then the area will be maximum = 200pi.

We cant take longest side as diameter because of different dimensions. So, 360pi is ruled out.

We cant take 8 in as the diameter, well in that case area = 192pi.
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24 Apr 2010, 06:28
The max. diameter possible in this case is 10
IMO 200pi
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24 Apr 2010, 07:36
Yes right, 10 will be max diameter and 8 as height.
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24 Apr 2010, 09:28
5 is the max radius possible. Therefore , 200*pi is the answer.
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24 Apr 2010, 09:53
ykaiim wrote:
IMO 200pi.

As all the dimensions are different. So. the key here is to find the maximum radius the circular faces. In this case if the cylinder is placed in vertical position with height = 8 and radius = 10/2 then the area will be maximux = 200pi.

"We cant take longest side as diameter because of different dimensions. So, 360pi is ruled out."

We cant take 8 in as the diameter, well in that case area = 192pi.

"[color=#BF0000]We cant take longest side as diameter because of different dimensions. So, 360pi is ruled out."[/color]

Why can't we take the largest side as diameter (r=6) in this case is my question? Please explain.

OA is 200pi.
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24 Apr 2010, 10:10
@srichaks,

See, if you take r=6 (diameter = 12) then try to think of the circular surface of the cylinder. The width of the cuboid = 10. Cylinder will not have the complete circular surface. See the attached diagram.

I hope you get my point.
Attachments

Circle.JPG [ 11.66 KiB | Viewed 2752 times ]

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24 Apr 2010, 10:50
ykaiim wrote:
@srichaks,

See, if you take r=6 (diameter = 12) then try to think of the circular surface of the cylinder. The width of the cuboid = 10. Cylinder will not have the complete circular surface. See the attached diagram.

I hope you get my point.

Yes. Thanks ykaiim!!
Re: Volume Cylinder   [#permalink] 24 Apr 2010, 10:50
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