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A rectangular box has dimensions 12*10*8 inches. What is the

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Re: A rectangular box has dimensions 12*10*8 inches. What is the  [#permalink]

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New post 26 Apr 2017, 13:49
I feel like this question carries a typo.
"what is the max value of the right cylinder"..
Value of a right cylinder????

Do they mean "volume" instead of "value"?
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Re: A rectangular box has dimensions 12*10*8 inches. What is the  [#permalink]

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New post 09 Jul 2018, 11:24
Shrivathsan wrote:
a doubt on basics :
it is a very silly question.
But why are we considering volume and not surface area ?
I got confused and made a blunder in the problem



probably, surface area cannot be the value of a cylinder

thanks
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Re: A rectangular box has dimensions 12*10*8 inches. What is the  [#permalink]

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New post 09 Jul 2018, 11:32
e z prob
Max r^2 h
5^2 * 8
Answer B

Next largest volume is 4^2 * 12 Pie
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A rectangular box has dimensions 12*10*8 inches. What is the  [#permalink]

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New post 28 Feb 2019, 06:33
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:
[https://gmatclub.com/forum/posting.php?mode=quote&f=140&p=1052687#b]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?[/b]

\(volume_{cylinder}=\pi{r^2}h\)

If 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 \(200\pi\).

Answer: B.

Similar question to practice: http://gmatclub.com/forum/the-inside-di ... 28053.html

Hope it helps.


bb I guess,It should be \(volume==\pi*{4^2}*12=192\pi\);
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A rectangular box has dimensions 12*10*8 inches. What is the   [#permalink] 28 Feb 2019, 06:33

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