Julie has a cylinder containing sugar. The cylinder has a volume of 288π cubic centimeters. Which of the following could be the dimensions of Julie's sugar container?

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.