A sphere has a diameters of 4.6cm and is placed in an full overflow cup and sinks to the bottom how much water was displaced by the sphere

To see how much it displaced, you basically just have to find the volume of the sphere. 

Given that the diameter is 4.6 which means that the radius is 2.3, the volume of the sphere is 50.965 or rounded up to 51.

The amount of water displaced by the sphere was 51cm^3.

Hope this helps :)