Question

An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 8 cm, and the height is 15 cm. Find the rate at which the water level is rising when the water level is 3 cm.

Answer 1

19.53125 cm/s

Explanation:

h : s

15 : 8

s/h = 8/15

s = 8h/15

V = ⅓×s²×h

V = ⅓(8h/15)²×h = 64h³/675

dV/dh = 64h²/225

At h=3,

dV/dh = 64(3²)/225 = 64/25

dh/dV = 25/64

dV/dt = 50

dh/dt = dh/dV × dV/dt

= 25/64 × 50

= 19.53125 cm/s

Answer 2

Explanation:

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