Cylinder vs Cone: Which Tank Empties First? | “SpaceX Interview Question?”

Which tank empties first — a cylinder or a cone? Imagine two tanks with the same height, the same top diameter, and identical openings at the bottom. Open both taps at the same time. Which one empties first? At first, there are two tempting answers: • Since the water height is the same, Torricelli's law suggests that the water should initially leave both tanks at the same speed. • The cone contains only one-third as much water as the cylinder, so perhaps it should empty three times faster. But neither argument gives us the actual emptying time. In this video, we use Torricelli's law together with conservation of volume to derive the complete draining time for both tanks. The interesting part is understanding *why*. The flow speed depends on the water height, but the cross-sectional area of the tank also changes as the water level falls — and in the cone, that geometry makes a huge difference. The question is sometimes presented online as a “SpaceX interview question,” so I've kept the question mark in the title and thumbnail rather than claiming that attribution as established fact. #Physics #Mathematics #FluidMechanics #Python #Calculus #Engineering