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

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 8 cm.

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

Answer 1

We must first find the volume equation of the shape, and then we must take derivatives of both sides with respect to time.

 

V = (l*w*h)/3

 

dV/dt = (1/3)(l*w)(dh/dt)

 

When height of the water level is 2 cm, that is 1/4 of the total height. Therefore the length and width at that point must also be 1/4 of the length & width of the base. Therefore:

 

l = 0.75 cm

w = 0.75 cm

 

70 cm³/sec = (1/3)(0.75 cm)(0.75 cm)(dh/dt)

 

dh/dt = (70 cm³/sec)/(0.1875 cm²) = 373.33 cm/sec