91Ó°ÊÓ

Find the volume of the solid generated by revolving each region about the \(y\) -axis. The region enclosed by the triangle with vertices (1,0),(2,1) and (1,1)

Find the volume of the solid generated by revolving each region about the \(y\) -axis. The region in the first quadrant bounded on the left by the circle \(x^{2}+y^{2}=3,\) on the right by the line \(x=\sqrt{3},\) and above by the line \(y=\sqrt{3}\)

Find the volume of the solid generated by revolving the region bounded by \(y=\sqrt{x}\) and the lines \(y=2\) and \(x=0\) about a. the \(x\) -axis. b. the \(y\) -axis. c. the line \(y=2\) d. the line \(x=4\)

By integration, find the volume of the solid generated by revolving the triangular region with vertices \((0,0),(b, 0),(0, h)\) about a. the \(x\) -axis. b. the \(y\) -axis.

A bowl has a shape that can be generated by revolving the graph of \(y=x^{2} / 2\) between \(y=0\) and \(y=5\) about the y-axis. a. Find the volume of the bowl. b. Related rates If we fill the bowl with water at a constant rate of 3 cubic units per second, how fast will the water level in the bowl be rising when the water is 4 units deep?

a. A hemispherical bowl of radius \(a\) contains water to a depth \(h\) Find the volume of water in the bowl. b. Related rates \(\quad\) Water runs into a sunken concrete hemispherical bowl of radius \(5 \mathrm{m}\) at the rate of \(0.2 \mathrm{m}^{3} / \mathrm{sec} .\) How fast is the water level in the bowl rising when the water is \(4 \mathrm{m}\) deep?