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a) A hemispherical tank with a radius of 18 meters is filled from an inflow pipe...

a) A hemispherical tank with a radius of 18 meters is filled from an inflow pipe at a rate of 8 cubic meters per minute. The depth of the water in the tank is changing at a rate of about 0.001 meters per minute. What is the rate of change of the exposed surface area of the water when the water is 9 meters​ deep?

b) A swimming pool is 50 m long and 20 m wide. Its depth decreases linearly along the length from 3 m to 1 m. It is initially empty and is filled at a rate of 1 mcubed​/min. How fast is the water level rising 160 min after the filling​ begins? How long will it take to fill the​ pool?

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