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.htmlHope it helps.