Can't the radius also be 5? since one of the sides is 10...
I labored over the same question the first time I saw this one.
The radius cannot be 5 unless 2 sides of the box have a dimension of 10.
If you draw the figure , it will make sense to you.
You can have a canister of diameter 8 which will use the face of 8X10 for its base and 6 for its hieght.
you can have a canister of diameter 6 which can use the face of either 6X8 or 6X10 for its base and the third dimension for its hieght.
Calculating volume , canister using base of 8X10 will have largest volume.
Hence diameter 8 or radius 4.
Hope that helps.