Question

6. A water tank is in shape of right circular cone with the height 30 ft and radius 8 ft at the top. Recall that 1 cubic foot of water weighs 62.4 lb. (pick h= 0 location so the setup is easier.) а. Write the integral to calculate the work required to pump all of the water over the top of the tank if the tank is full. b. If the tank is filled with water to a depth of 20 ft. Write the integral to calculate the work required to remove all the water over the top of the tank. c. If the tank is full write the integral to calculate the work required to pump out water over the top of the tank to a level of 10 feet (left in the tank). d. The tank is full of water. Write the integral to calculate the amount of work required to pump all the water out to a height of 10 ft above the top of the tank. e. The tank is half full. Write the integral to calculate the amount of work required to pump all the water out to a height of 10 ft above the tank.

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