Think about what would give you the largest volume? Pi r^2 h. You want the radius as large as possible, since it's being squared. But be careful, I made this mistake when I did this question a couple weeks ago. If the side that 12x10 is laying down, the diameter isn't 12, it's 10. So, half of the diamater of 10 is 5. 5^2x hpi = 25x8xpi.

The Best way to solve this is by drwaing the diagram.

Diag 1: Base = 12 * 8 ==>> What is max radius?? => 4 (because if radius is 6 it will go out of the box from other side which is 8). ==> Height = 10 ===> Vol = pi * 16 *10 = 160 pi

Diag 2: Base = 10 * 8 ==>> What is max radius?? => 4 (because if radius is 5 it will go out of the box from other side which is 8). ==> Height = 12 ===> Vol = pi * 16 *12 = 192 pi

Diag 3: Base = 12 * 10 ==>> What is max radius?? => 5 (because if radius is 6 it will go out of the box from other side which is 10). ==> Height = 18 ===> Vol = pi * 25 *8 = 200 pi