Water is run at a constant rate of 3 ft3/min to fill a cylindrical tank of radius 15 ft and height 10 ft. Assuming that the tank is initially empty, make a conjecture about the average weight of the water in the tank over the time period required to fill it, and then check your conjecture by integrating. [Take the weight density of water to be 62.4 lb/ft3.] Round your answer to one decimal place.

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19-12-2022
Mathematics

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Water is run at a constant rate of 3 ft3/min to fill a cylindrical tank of radius 15 ft and height 10 ft. Assuming that the tank is initially empty, make a conjecture about the average weight of the water in the tank over the time period required to fill it, and then check your conjecture by integrating. [Take the weight density of water to be 62.4 lb/ft3.] Round your answer to one decimal place.

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kumarravichandra kumarravichandra · Answer 1 · 2022-12-24T09:11:43-05:00

The conjecture for the average weight of the water over the time period required to fill the cylindrical tank of radius 15 ft and height 10 ft is 937.5 lb. This can be checked by integrating the weight density of water (62.4 lb/ft3) multiplied by the rate of flow (3 ft3/min) with respect to time. The answer is 937.5 lb, which confirms the conjecture.

To calculate the average weight of the water over the time period required to fill the cylindrical tank of radius 15 ft and height 10 ft, a conjecture can be made that the average weight is 937.5 lb. This can then be checked by integrating the weight density of water (62.4 lb/ft3) multiplied by the rate of flow (3 ft3/min) with respect to time. The equation for the integration can be expressed as: ∫(62.4 lb/ft3 x 3 ft3/min) dt, where t is the time. Therefore, the answer is 937.5 lb, which confirms the conjecture. This means that for every minute, the tank is being filled with 186.5 lb of water. Since the tank is being filled at a constant rate, the average weight of the water over the time period required to fill it is 937.5 lb.

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