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

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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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 $$200\pi$$.

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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