A hole of diameter d is drilled through a sphere of radius r in such a way that the axis of the hole passes through the centre of the sphere. Find the volume of the solid that remains.

I drew a picture of a sphere centred on the cartesian plane, with a hole going through its centre (in the shape of a cylinder).

I already knew that the volume of the sphere was . I then worked out the volume of the hole (cylinder):

Volume of solid remaining =

but the correct answer was

I cant see where I went wrong cause surely the objective of this problem is to minus the hole (cylinder) from a sphere to get the remaining volume?