# Volume of a Solid of Revolution

Volume of a solid generated by the rotating the region formed by the graphs - y= x^2 , y =2, x = 0

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A volume of a solid of revolution is found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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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