jmc

We must find the radius of the circle in order to find the area. We are told that points $A$ and $B$ are the endpoints of a diameter, so we can find the distance between these two points. We use the distance formula: $\sqrt{(7-3{)}^2+(10-5{)}^2}=\sqrt{16+25}=\sqrt{41}$.

Since the diameter has a length of $\sqrt{41}$, the radius must have length $\sqrt{41}/2$. Therefore, the answer is $(\sqrt{41}/2{)}^2\pi =\boxed{\frac{41\pi }{4}}$.