We can use the formula for the volume of a cube to solve this problem. Since the refrigerator has a square base with sides that are 3 feet long, the area of the base is 3 x 3 = 9 square feet.
Let's assume that the height of the refrigerator is h feet. Then, the volume of the refrigerator can be expressed as:
V = 9h = 40.5
Solving for h, we get:
h = 40.5/9 = 4.5 feet
Therefore, the refrigerator is 4.5 feet tall.