A water tank in the shape of a right circular cone shown ...



1. A water tank in the shape of a right circular cone has a height of 30 ft and a radius of 6 ft. Set up the integral for the work done in each case. Your integral must correspond to the variable indicated in the picture. The density of water is 62.4 lb/cubic ft.

A. The tank is full of water and the water is pumped over the top of the tank.

Volume of the slice/layer =

Weight of the slice =

Work done to move the slice to the top =

Total work done =

B. The initial depth of the water in the tank is 20 ft and the water is pumped over the top of the tank.

Volume of the slice/layer =

Weight of the slice =

Work done to move the slice to the top =

Total work done =

C. The tank is full of water and water is pumped to a height of 5 ft above the top of the tank

Volume of the slice/layer =

Weight of the slice =

Work done to move the slice to the top =

Total work done =

D. The tank is full, and the water is pumped to a point on top of the tank until the water level drops to 10 ft in the tank.

Volume of the slice/layer =

Weight of the slice =

Work done to move the slice to the top =

Total work done =

2. Repeat the steps in problem 1 for a cylindrical tank where the slice is at a height h from the base of the cylinder.

A.

[pic]

B.

[pic]

C.

[pic]

D.

[pic]

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