# Application of integration

1. A cylindrical tank of diameter 5ft and height 10 ft is full of water. The water is pumped out over the top. Find the work required to

a. Empty the entire tank.

B. Empty half of the tank.

https://brainmass.com/math/integrals/application-integration-228972

#### Solution Preview

Let us consider a layer of water dy thick at a depth y from the top. Let weight of the water in the layer be dw. In order to evacuate this water layer from the top, the water has to be raised to a height of y ft and the work required to be done for doing so is equal to the increase in the potential energy of the water layer.

Work done in raising dw weight of water through a height y ft = ydw

dw = Volume of water in ...

#### Solution Summary

The expert uses the application of integration to determine the work required to empty the entire cylindrical tank or empty half of the tank. A step by step solution provided.