Volume Examples

Volume Examples

Here is a Maple Worksheet that investigates the volume of a solid of revolution including looking at sums of volumes of cross section cylinders. In the worksheet the interval is [ -1 , 2 ] and each x_i is the midpoint of the ith subinterval. Thus if there are n equal length subintervals then the length of each subinterval will be 3/n and each x_i will be given by -1 + (3/n)(i - 0.5). Quicktime Animation

Example 1

Find the volume of the solid formed by revolving the region bounded by the graphs of the equations given below about the x-axis. DPGraph Picture

Example 2

Find the volume of the solid formed by revolving the region in Example 1 about the line y = -2.

Click here to see a picture of the two surfaces that form the sides of the solid. DPGraph Version

Example 3

Find the volume of the solid formed by revolving the region bounded by the graphs of the equations given below about the y-axis. DPGraph Picture

Example 4

Find the volume of the solid formed by revolving the region bounded by the graphs of the equations given below about the x-axis. DPGraph Picture

Example 5

Find the volume of the solid whose base is bounded by the graphs of the equations given below and whose cross sections are equilateral triangles perpendicular to the x-axis.

Example 6

Shell Method Example: Find the volume of the solid formed by revolving the region bounded by the graphs of the equations given below about the line x = -1.

Example 7

Find the volume of the solid formed by revolving the region bounded by the graphs of the equations given below about the x-axis. DPGraph Picture

Example 8

Shell Method Example: Find the volume of the solid formed by revolving the region bounded by the graphs of the equations given below about the line y = -2.

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Lane Vosbury, Math Chair, Seminole Community College email: vosburyl@scc-fl.edu