Thanks Find the volume of the solid generated by rotating the region bounded by

Question

Thanks

Find the volume of the solid generated by rotating the region bounded by the curves y = x2/3 + 1, x = 8, x = - 1 and the x-axis about the x -axis. A tank full of water has the shape of a paraboloid of revolution as in the figure below; that is, its shape is obtained by rotating a parabola about a vertical axis. If its height is 4 ft and the radius at the top is 4 ft, find the work required to pump the water out of the tank. A stone is dropped from a height of 256ft. Find its mean velocity. (g = 32 ft/s2)

Explanation / Answer

Shell method: V = 2? ? r h dr {a,b} .......... limits in {}
radius is (1+y) to rotate around y=-1

Disc method: V = ? ? f(x)

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