A swimming pool is in the shape of a circle with diameter $60$ ft. The depth varies linearly along the east-west direction from $3$ ft at the shallow end in the east to $15$ ft at the diving end in the west (this is so that divers look impressive against the sunset) but does not vary at all along the north-south direction. What is the volume of the pool, in $\mathrm{ft}^{3}$?