A water tank is spherical in shape with radius of 90 feet. Suppose the tank is...

A water tank is spherical in shape with radius of 90 feet. Suppose the tank is filled to a depth of 140 feet with water. Some of the water will be pumped out and, at the end, the depth of the remaining water must be 40 feet.

i) Set up a Riemann sum that approximates the volume of the water that is pumped out of the tank. (use horizontal slicing). You have to draw a diagram and choose a coordinate system to associate with the diagram.

ii) Set up, but do NOT evaluate, the integral for the volume of the water that is pumped out of the tank.

iii) Suppose the tank is filled at the depth of 140 feet with water. (Use the fact that water weighs approximately 62.4 lbs) . Some of the water is to be pumped out through a spout that is 6 feet over the top of the tank. The depth of the water remaining at the end is 40 feet. Set up (do not evaluate) the definite integral for the work required to pump the water out of the spout.

Solutions

Expert Solution

The coordinate axis is taken as center of spherical water tank. With x- axis parallel to water surface.

Therefore 40feet depth from the center is taken.

If it is total depth than integration must be from -50 to +50 everywhere in above image.

milcah answered 1 year ago

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