Inverted Pyramid Being Filled

Question

An inverted pyramid is being filled with water at a constant rate of 40 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 5 cm, and the height is 9 cm.

Find the rate at which the water level is rising when the water level is 2 cm.

Answer 1

s: side length of square then s = 5/9·h

V = 1/3·(5/9·h)²·h = 25/243·h³

dV/dt = 25/81·h²·dh/dt = 40

h=2: dh/dt = 32.4 cm/sec