Calculus I Related Rates Problem (An inverted pyramid is being filled with water at a constant rate)

Question

An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 2 cm, and the height is 9 cm.

Find the rate at which the water level is rising when the water level is 6 cm.

Answer 1

Volume v = a²h/3; dv/dt = a²(dh/dt)/3; dh/dt = (3dv/dt)/(a²) = 3·35cm³/s/(4cm²) = 26.25 cm/s

Rate of change of level is constant