Problem 1

Find the volume of the solid that results when the region bounded by $y=\sqrt{9-x^{2}}$ and the $x$ -axis is revolved around the $x$ -axis.

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Problem 2

Find the volume of the solid that results when the region bounded by $y=$ sec $x$ and the $x$ -axis from $x=-\frac{\pi}{4}$ to $x=\frac{\pi}{4}$ to is revolved around the $x-$ axis.

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Problem 3

Find the volume of the solid that results when the region bounded by $x=$ $1-y^{2}$ and the $y$ -axis is revolved around the $y$ -axis.

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Problem 4

Find the volume of the solid that results when the region bounded by $x=$ $\sqrt{5} y^{2}$ and the $y$ -axis from $y=-1$ to $y=1$ is revolved around the $y$ -axis.

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Problem 5

Use the method of cylindrical shells to find the volume of the solid that results when the region bounded by $y=x, x=2,$ and $y=-\frac{x}{2}$ is revolved around the $y$ -axis.

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Problem 6

Use the method of cylindrical shells to find the volume of the solid that results when the region bounded by $y=\sqrt{x}, y=2 x-1,$ and $x=0$ is revolved around the $y$ -axis.

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Problem 7

Use the method of cylindrical shells to find the volume of the solid that results when the region bounded by $y=x^{2}, y=4,$ and $x=0$ is revolved around the $x$ -axis.

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Problem 8

Use the method of cylindrical shells to find the volume of the solid that results when the region bounded by $y=2 \sqrt{x}, x=4,$ and $y=0$ is revolved around the $y$ -axis.

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Problem 9

Find the volume of the solid whose base is the region between the semicircle $y=\sqrt{16-x^{2}}$ and the $x$ -axis and whose cross-sections perpendicular to the $x$ -axis are squares with a side on the base.

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Problem 10

Find the volume of the solid whose base is the region between $y=x^{2}$ and $y=4$ and whose perpendicular cross-sections are isosceles right triangles with the hypotenuse on the base.

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