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Greg Kelly, Hanford High School, Richland, Washington

Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. 7.3 day 2. Disk and Washer Methods. Limerick Nuclear Generating Station, Pottstown, Pennsylvania. Suppose I start with this curve.

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Greg Kelly, Hanford High School, Richland, Washington

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  1. Photo by Vickie Kelly, 2003 Greg Kelly, Hanford High School, Richland, Washington 7.3 day 2 Disk and Washer Methods Limerick Nuclear Generating Station, Pottstown, Pennsylvania

  2. Suppose I start with this curve. My boss at the ACME Rocket Company has assigned me to build a nose cone in this shape. So I put a piece of wood in a lathe and turn it to a shape to match the curve.

  3. The area of each slice: How could we find the volume of the cone? One way would be to cut it into a series of thin slices (flat cylinders) and add their volumes.

  4. This application of the method of slicing is called the disk method. The shape of the slice is a disk, so we use the formula for the area of a circle to find the volume of the disk. If the shape is rotated about the x-axis, then the formula is:

  5. The region between the curve , and the y-axis is revolved about the y-axis. Find the volume. y x The radius is the x value of the function .

  6. Homework Section 7.3 P392 #13,14,17-20, 29,30

  7. Find the volume of the solid generated by revolving the region bounded by the curves about the x-axis. Do not use a calculator.

  8. The area of the washer is: The region bounded by and is revolved about the y-axis. Find the volume. If we use a horizontal slice: The “disk” now has a hole in it, making it a “washer”. outer radius inner radius

  9. Find the volume of the solid generated by revolving the region bounded by the curves about the x-axis.

  10. The washer method formula is: This application of the method of slicing is called the washer method. The shape of the slice is a circle with a hole in it, so we subtract the area of the inner circle from the area of the outer circle.

  11. Homework Section 7.3 Page 392 #21-26,31-34 all

  12. Find the volume of the solid generated by revolving the region bounded by the curves • about the x-axis. • about the y-axis.

  13. Find the volume of the solid generated by revolving the region bounded by the curves about the line

  14. Find the volume of the solid generated by revolving the region bounded by the curves • about the x-axis. • about the line • about the

  15. Homework Best Book 8.2 #1-20 all

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