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

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.

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

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

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