I came across the following

MGMAT geometry question which looks relatively straight forward at first-

A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the largest possible volume of a right circular cylinder that can be placed inside the box?I calculated the answer as follows:

for the cylinder, r= 12/2 =6 and h=10 => area = \pi*r^2*h = \pi*6^2*10 = 360*\pi

However the MGMAT solution to this says that the radius can only be taken as 4 or 5 and hence the right answer is \pi*5^2*8=200*\pi

I am stumped about why they not considering the 12 inch dimension.. is there something obvious I am missing here?

thanks in advance!