Anthony has a sink that is shaped like a half-sphere

I think you are referring to this:
The volume of the sink shaped like a half sphere is [2000/3] π in^2.

A. The volume of a cylinder =area of the base * height
For this part the cup has a diameter, d, of 4 in and height, h, of 8 in.
[2000 / 3]π / [32π] = 20.83
21 cups.

B. For this part the diameter of the cup is 8 in and the height is 8 in
And the number of cups needed is [2000π/3] / (128π) = 5.2
5 cups

The answer would be the second choice : )