An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per second.

Question

An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 3 cm, and the height is 10 cm.

Find the rate at which the water level is rising when the water level is 7 cm.

Answer 1

Draw a figure. The side of the square is dependent on the height as follows

h/(s/2) = 10/(3/2) i.e. s = 3h/10.

The volume V(t) remaining at any time is h(t)*s²(t) = h*9h²/100

and dV/dt = (9/100)*3h² (dh/dt)

Now just plug in the values from the problem to get the answer.