3. A swimming pool is in the shape of a circle with diameter $60 \mathrm{ft}$. The depth varies linearly along the east-west direction from $3 \mathrm{ft}$ at the shallow end in the east to $15 \mathrm{ft}$ 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 $\mathrm{ft}^{3}$ ?
Solution:
$$
8100 \pi
$$

Take another copy of the pool, turn it upside-down, and put the two together to form a cylinder. It has height $18 \mathrm{ft}$ and radius $30 \mathrm{ft}$, so the volume is $\pi(30 \mathrm{ft})^{2} \cdot 18 \mathrm{ft}=$ $16200 \pi \mathrm{ft}^{3}$; since our pool is only half of that, the answer is $8100 \pi \mathrm{ft}^{3}$.