Question

The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has maximum volume? (a)

Answer 1

If the cylinder is placed on 6*8 face then it's maximum radius is 6/2=3 and ;

If the cylinder is placed on 6*10 face then it's maximum radius is 6/2=3 and ;

If the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and ;

So, the maximum volume is for

P.S. Notice that radii of 5, 6, and 8 (options C, D and E) are not possible.