To find the maximum number of full cups of water that can be placed in the container without it overflowing, we need to determine how many cups can fit in each dimension and then multiply the results.
First, let's figure out how many cups can fit in terms of width. The width of the container is 10 inches, while the diameter of the cup is 4 inches (twice the radius). The cup cannot fit widthwise, as 4 inches is greater than 10 inches.
Next, let's consider the length of the container. The length is 15 inches, which is less than twice the cup's diameter (8 inches). Thus, the cup can fit lengthwise.
Now, we need to determine how many cups can fit in terms of height. The height of the container is 20 inches, while the height of the cup is 5 inches. 20 divided by 5 equals 4. So the cup can fit 4 times in terms of height.
Since the cup can fit once lengthwise and four times heightwise, the maximum number of cups that can fit in the container is 1 x 4 = 4 cups.