🧪 Mathematics Calculus Simulation

A classic calculus related-rates problem rendered as a live 3D simulation. Water drains from a conical tank at a constant volumetric rate you control, and because the tank narrows toward its apex, the water level does not fall at a constant speed — implicit differentiation of V = (πR²/3H²)h³ shows that dh/dt depends on 1/h², so the surface drops slowly while the tank is full and much faster as it nears empty. Adjust the drain rate and the tank's taper, watch the cone-shaped water body shrink in real time, and read the exact instantaneous dh/dt computed analytically from the chain rule at every frame alongside the current height, volume and surface radius.