An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 6 cm, and the height is 13 cm. Find the rate at which the water level is rising when the water level is 4 cm.

13.20 cm/s is the rate at which the water level is rising when the water level is 4 cm.

Explanation:

Length of the base = l

Width of the base  =  w

Height of the pyramid = h

Volume of the pyramid =

We have:

Rate at which water is filled in cube =

Square based pyramid:

l = 6 cm, w = 6 cm, h = 13 cm

Volume of the square based pyramid = V

Differentiating V with respect to dt:

Putting, h = 4 cm

13.20 cm/s is the rate at which the water level is rising when the water level is 4 cm.

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