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A rectangular box has dimensions 12*10*8 inches. What is the [#permalink]
 25 Apr 2006, 18:54
Question Stats:
25% (00:00) correct
75% (01:30) wrong based on 1 sessions
A rectangular box has dimensions 12*10*8 inches. What is the largest possible value of right cylcinder that can be placed inside the box?
Last edited by Bunuel on 02 Mar 2012, 03:11, edited 1 time in total.
Edited the question
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Voluem of cylinder is pi * r^2 * h
Obviously, we can get the largest value if r or h are two of the largest value used.
Let's try r = 12, h = 10, v = pi*36*10 = 360pi
And let's try r = 10, h = 12, v = pi*25*12 = 300pi.
The largest possible is therefore 360pi cubic-inches
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I am getting maximum area as 200 pi..with r = 5 and h = 8
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My ans is h=8, r=5, volume=200pi.
(If h=12, r can't be more than 4. So pi*r^2*h=12*16pi=192pi
Apparently h=10, r=4 can't be more
Since vol. involves r^2, looking for a greater r would help. However r can't be 6 because the max possible length of the other side could be only 10 which could not fit a circular base)
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Remember: the base of the cylinder is a circle
r is constant around the circle, so the base can completely fit in a square, not a rectangle. Therefore, you will not be able to use the entire space in the base of the rectangular box.
the volume of a cylinder is pi * r^2 * h
select largest possible r such that the dimensions of the rectangular base allow maximum value or r
you would want to maximize r more than h because r is squared here
so, select bases 10 and 12 allowing a maximum value of r = 5
volume of cylinder: 25 pi * 8 = 200 pi
to check, think if 8 is one of the dimensions of the base, r = 4
volume of cyclinder: 16 pi * (either 10 or 12 ) = 160 pi or 192 pi
not maximum volume
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max vol answer is 200pi with r = 5, and height = 8
other are clearly lower,
r = 4, h = 12
r = 4, h = 10
u have to take care of the different sides of the box while calculating the volume...
to ncprasad's concern, a diagonal long cylinder can't be fit into the box unless it becomes a think stick...
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12 by 10, determines the radius of the cylinder = 10/2 = 5
So height 8
Ans 200pi
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yes the OA is 200pi... but i got trapped along with ywilfred by maximizing the Volume algebratically... and the trap was logical sense 
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Re: Cylinder inside rectangular box refresher! [#permalink]
01 Mar 2012, 23:26
Why cant we have radius =6 and height = 10
making the volume 360 Pi ?
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Re: Cylinder inside rectangular box refresher! [#permalink]
02 Mar 2012, 03:19
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Ashamock wrote: Why cant we have radius =6 and height = 10 making the volume 360 Pi ? Dimensions of the box are 12*10*8 inches if radius of a cylinder is 6 then its diameter is 12 and it won't fit on any face of a box. For example it can not fit on 12*10 face of the box since diameter=12>10=side. Complete solution: A rectangular box has dimensions 12*10*8 inches. What is the largest possible value of right cylcinder that can be placed inside the box?volume_{cylinder}=\pi{r^2}hIf the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and volume==\pi*{4^2}*12=196\pi; If the cylinder is placed on 8*12 face then it's maximum radius is 8/2=4 and volume==\pi*{4^2}*10=160\pi; If the cylinder is placed on 10*12 face then it's maximum radius is 10/2=5 and volume==\pi*{5^2}*8=200\pi; So, the maximum volume is for 200\pi. Similar question to practice: the-inside-dimensions-of-a-rectangular-wooden-box-are-128053.htmlHope it helps.
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Re: Cylinder inside rectangular box refresher! [#permalink]
13 Jun 2012, 22:21
Bunuel wrote: Ashamock wrote: Why cant we have radius =6 and height = 10 making the volume 360 Pi ? Dimensions of the box are 12*10*8 inches if radius of a cylinder is 6 then its diameter is 12 and it won't fit on any face of a box. For example it can not fit on 12*10 face of the box since diameter=12>10=side. Complete solution: A rectangular box has dimensions 12*10*8 inches. What is the largest possible value of right cylcinder that can be placed inside the box?volume_{cylinder}=\pi{r^2}hIf the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and volume==\pi*{4^2}*12=196\pi; If the cylinder is placed on 8*12 face then it's maximum radius is 8/2=4 and volume==\pi*{4^2}*10=160\pi; If the cylinder is placed on 10*12 face then it's maximum radius is 10/2=5 and volume==\pi*{5^2}*8=200\pi; So, the maximum volume is for 200\pi. Similar question to practice: the-inside-dimensions-of-a-rectangular-wooden-box-are-128053.htmlHope it helps. Hi, Can you explain why the diameter cannot be 12 ?I am not getting the concept clearly...Thanks
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Re: Cylinder inside rectangular box refresher! [#permalink]
14 Jun 2012, 00:12
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farukqmul wrote: Bunuel wrote: Ashamock wrote: Why cant we have radius =6 and height = 10 making the volume 360 Pi ? Dimensions of the box are 12*10*8 inches if radius of a cylinder is 6 then its diameter is 12 and it won't fit on any face of a box. For example it can not fit on 12*10 face of the box since diameter=12>10=side. Complete solution: A rectangular box has dimensions 12*10*8 inches. What is the largest possible value of right cylcinder that can be placed inside the box?volume_{cylinder}=\pi{r^2}hIf the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and volume==\pi*{4^2}*12=196\pi; If the cylinder is placed on 8*12 face then it's maximum radius is 8/2=4 and volume==\pi*{4^2}*10=160\pi; If the cylinder is placed on 10*12 face then it's maximum radius is 10/2=5 and volume==\pi*{5^2}*8=200\pi; So, the maximum volume is for 200\pi. Similar question to practice: the-inside-dimensions-of-a-rectangular-wooden-box-are-128053.htmlHope it helps. Hi, Can you explain why the diameter cannot be 12 ?I am not getting the concept clearly...Thanks Sure. If the diameter is 12 then it won't fit on any face of the box. For example it can not fit on 12*10 face of the box since diameter=12>10=side. Hope it's clear.
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A rectangular box has the dimensions 12 inches x 10 inches x [#permalink]
25 Nov 2012, 08:25
Reference: Manhattan Geometry guide
A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the
largest possible volume of a right cylinder that is placed inside the box?
A.180 pie
B.200 Pie
C.300 Pie
D.320 Pie
E.450 Pie
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Re: A rectangular box has the dimensions 12 inches x 10 inches x [#permalink]
25 Nov 2012, 08:34
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Re: A rectangular box has the dimensions 12 inches x 10 inches x
[#permalink]
25 Nov 2012, 08:34
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