Value based question - needs a UNIQUE value.

(1) - Height is not given -> so insufficient.
So, eliminate AD [If you don't know this strategy, then read it in Manhattan or watch a youtube video]

(2) - Longest distance in a cylinder is the hypotenuse, which is, the length between one end of the radius of the top to the other end of the radius of the bottom.

Now, in a right angled triangle, we have a hypotenuse =13, then other two sides will be 5 and 12.
This is sufficient.

Combination of (1) & (2) is not required.
Hence, B is the answer.

Given that height > Diameter

Target Question=> What is the volume of the cylinder?
$$volume\ =\pi r^2h$$
Therefore, height >2r because d=2r
Statement 1=> The radius of the base is 2.5.
Height is unknown, so, the target question cannot be evaluated. Statement 1 is NOT SUFFICIENT.

Statement 2=> The longest distance between any two points on the cylinder is 13.
The longest between any two points is the diagonal and it can be also said to be the hypotenuse of a right triangle formed by the height and diameter as the base and with Pythagoras, as we get a triplet value of 5, 12 and 13. I,e base/diameter = 5, and height = 12.
Since d=2r, r=d/2 = 5/2 = 2.5
$$So,\ volume,\ v\ =\ \pi r^2h$$
$$v\ =\ \frac{22}{7}\cdot2.5^2\cdot12$$
$$v\ =\ 236$$
Statement 2 alone is SUFFICIENT. Hence, option B is the correct answer.