Zadanie 10d, Paper 2, maj 2022, TZ1, Matematyka AA IB HL

Let $f(x)=\sqrt{x^2-4}$ for 2≤x≤3. Rotating its graph around the y-axis gives the outer wall of a vessel, with x representing radial distance and y height in metres. A solid vertical cylinder of radius 1 m stands along the vessel axis from bottom to top. Water occupies the annular space outside this cylinder and inside the outer wall. A flat bottom seals the vessel at y=0. Initially empty, it is filled at 0.5 m³/s.