An inverted pyramid is being filled with water at a rate of 45 cubic cm/sec. The pyramid top is square with sides 5 cm and the height is 11 cm. Find the rate of the water level rising when it's 5 cm.

Question

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 5 cm, and the height is 11 cm.

Find the rate at which the water level is rising when the water level is 5 cm.

Answer 1

Let h is water level. Then base area B/25 = h²/11²; B = 25h²/121; volume V = Bh/3 = 25h³/363;

dV/dt = 25h²/121·dh/dt; dh/dt = 121dV/dt/(25h²) = 121·45cm³/s/(625cm²) = 8.712 cm/s