the maximum possible distance will be from the bottom-right corner to the top-left corner OR vice-versa.

This distance is merely the diagonal, which can be considered to be the hypotenuse of a right angled triangle and thus calculated using the Pythagoras theorem

the base will be the diameter = 3+3 = 6
height = 3

--> diagonal (hypotenuse) = √(6^2 + 3^2) = √[(3^2)(2^2 + 1)] = √[(3^2)(5)]

--> diagonal = 3√5 ......[spoiler]choice (B)[/spoiler]

sanju09 wrote:A right circular cylinder has radius 3 and height 3. If A and B are two points on its surface, what is the maximum possible straight-line distance between A and B?
(A) 3 √6
(B) 3 √5
(C) 6
(D) 3 √3
(E) 3 √2

Diameter is 6
height is 3

So length of hypotenuse is root(36+9) = root(45) = 3root(5)

root of (6^2+3^2)=root of 45= 3 √5