Related Rates: An Inverted Pyramid is Being Filled

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 4 cm, and the height is 7 cm. Find the rate at which the water level is rising when the water level is 4 cm.

Answer 1

Let V is volume of water: V = 1/3hA; A/16 = h²/49; A = 16h²/49 and V = 16h³/147;

dV/dt = 48h²(dh/dt)/147 = 16h²(dh/dt)/49; dh/dt = (dV/dt)·49/(16h²) = 35cm³/s·49/(16·16cm²) = 6.7 cm/s