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An oil tank has the shape of a cylinder with a diameter of 10 feet. It is mounted so that the axis of the cylinder is horizontal (the circular cross-sections of the cylinder are vertical). If the depth of the oil is 6 feet, what percentage of the total capacity of the tank is filled? After drawing a picture and setting up this problem, use the following methods to find a numerical estimate and answer.

a) Use geometric techniques to estimate the percentage full. Find an upper and lower bound to the percentage full.

b) Use analytical methods to evaluate the integral in part a.

 

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