# Volume of solids of revolution

Volume of solids of revolution..

1. A paraboloid dish (cross section ) is 8 units deep. It is filled with water up to a height of 4 units. How much water must be added to the dish to fill it completely?

4. Write an integral that represents the volume of the solid formed by rotating the region bounded by , , , and about (a) the axis; (b) the line ; and (c) the line , where .

15. Consider the solid formed by rotating the curve from to about the axis. Let be the function whose value is the volume of the solid between and . (a) What is ? (b) For some small , what is ? (c) Using the definition of the derivative, find the definite integral that represents the total volume of the solid. (Let be a function such that .)

26. Find the volume of the top quarter of a sphere: .

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#### Solution Summary

Several volumes of solids of revolution are calculated, and the general formula for the volume of such a solid is derived. Step by step explanation for the method used is given

The solutions are given in a PDF file.