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605-655 Level|   Geometry|      
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guialain
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A rectangular box has dimensions 12*10*8 inches. What is the 26 Apr 2017, 13:49
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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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A rectangular box has dimensions 12*10*8 inches. What is the 09 Jul 2018, 11:24
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Shrivathsan
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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A rectangular box has dimensions 12*10*8 inches. What is the 09 Jul 2018, 11:32
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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 28 Feb 2019, 06:33
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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: https://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 18 Jun 2019, 00:24
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willget800
A rectangular box has dimensions 12*10*8 inches. What is the largest possible value of right cylinder that can be placed inside the box?

A. 180 pie
B. 200 Pie
C. 300 Pie
D. 320 Pie
E. 450 Pie

THE EXPLANATION IS AS ATTACHED.

ANSWER: OPTION B
Attachments

Screenshot 2019-06-18 at 12.53.56 PM.png
Screenshot 2019-06-18 at 12.53.56 PM.png [ 409.46 KiB | Viewed 2585 times ]

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A rectangular box has dimensions 12*10*8 inches. What is the 04 Aug 2019, 08:56
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RobVanDam
Bunuel
Ashamock
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: https://gmatclub.com/forum/the-inside-di ... 28053.html

Hope it helps.

bb I guess,It should be \(volume==\pi*{4^2}*12=192\pi\);

RobVanDam is right
Could someone please ask Bunuel to edit that to 192\(\pi\)
I guess this is going to be the rarest of rare occasions when Bunuel did a mistake, no he can't - It might have been just a typo error :)
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A rectangular box has dimensions 12*10*8 inches. What is the 04 Aug 2019, 12:03
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DarkHorse2019
RobVanDam is right
Could someone please ask Bunuel to edit that to 192\(\pi\)
I guess this is going to be the rarest of rare occasions when Bunuel did a mistake, no he can't - It might have been just a typo error :)

Typo edited. Thank you.

Errare humanum est. :)
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A rectangular box has dimensions 12*10*8 inches. What is the 13 Sep 2020, 03:24
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willget800
A rectangular box has dimensions 12*10*8 inches. What is the largest possible value of right cylinder that can be placed inside the box?

A. 180 pie
B. 200 Pie
C. 300 Pie
D. 320 Pie
E. 450 Pie

The question is a bit confusing when it says "largest possible value of right cylinder". Value could mean anything, better to state 'volume' directly.

Approaching this question, we need to think of different constraints as we set up the right cylinder.
To maximize the volume we need to maximize the radius and height of the right cylinder.

Case #1
Base of the box is 12X10 -> Radius of right cylinder = 5
Height of box = height of cylinder = 8
Cylinder volume = (5^2)*8*pi = 200*Pi (OA B)

Case #2
Base of the box is 10X8 -> Radius of right cylinder = 4
Height of box = height of cylinder = 12
Cylinder volume = (4^2)*12*pi = 192*Pi

Case #3
Base of the box is 12X8 -> Radius of right cylinder = 4
Height of box = height of cylinder = 10
Cylinder volume = (4^2)*10*pi = 160*Pi


Note the Radius of the right cylinder cannot be 6 as the base is not a square of 12X12
The smallest side of the rectangle determines the radius
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A rectangular box has dimensions 12*10*8 inches. What is the 20 Feb 2023, 09:09
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