Answer true or false. Water is running out of an inverted conical tank so the height is changing at a rate of 4 ft/s. The height of the water in the tank is changing at 4 ft/s if the height is currently 10 ft and the radius is 8 ft.

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Quizplus · Accepted Answer

Since the tank is conical, we can use the formula V = (1/3)πr^2h to relate the volume of water in the tank to its height. Taking the derivative with respect to time, we get dV/dt = (1/3)πr^2(dh/dt). We know that dV/dt is negative (since water is running out of the tank), and we are given that dh/dt = -4 ft/s. Plugging in r = 8 ft and h = 10 ft, we can solve for dH/dt to get -6.28 ft/s. Since the rate of change of height is negative, we take the absolute value to get the final answer of 6.28 ft/s.

Answer True or False