Everything here revolves around the formula for the volume of a cylinder of radius r and height h:
V = pi*r^2*h
Here, V= 288*pi cubic cm = pi*r^2*h, or
288 = r^2*h
Unfortunately, you have not shared the answer choices. But I can invent values for r and h and find the corresponding h and r:
Suppose that r = 5 cm. Then r^2 = 25 cm^2, and (25 cm^2)*h = 288 cm^3. Solving for h,
288 cm^3
h = ---------------- = 11.52 cm
25 cm^2
Look at the given possible answers and check out each set, one by one, in the same manner.