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Volumes using washers

Volumes using washers. Now that you have successfully designed a 4 by 4 meter nose cone, your boss brings to you a larger nose cone that is 16 meters long by 8 meters wide. .

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Volumes using washers

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  1. Volumes using washers

  2. Now that you have successfully designed a 4 by 4 meter nose cone, your boss brings to you a larger nose cone that is 16 meters long by 8 meters wide. In order to safely ship it, you need to cover it with a layer of insulation exactly as thick as shown in the gray area below: What you know about the design is that the curvature of the nose cone and the insulation can be given by…

  3. Now that you have successfully designed a 4 by 4 meter nose cone, your boss brings to you a larger nose cone that is 16 meters long by 8 meters wide. In order to safely ship it, you need to cover it with a layer of insulation exactly as thick as shown in the gray area below: How many cubic meters of insulation will it take to make this layer?

  4. Rotate the region about the x-axis If we use vertical slices The “disks” now have holes in them, making them more like “washers”. We find the volume of a washer by considering it to be two disks; an outer and inner disk. We find the volume by subtracting the volume of the hole from the volume of the disk.

  5. R The volume of the disk is R2 r The volume of the hole is r2 When we subtract, we get… dx outer radius inner radius

  6. The volume of the washer is: The region bounded by and is revolved about the y-axis. Find the volume. outer radius inner radius

  7. r R If the same region is rotated about the line x=2: The outer radius is: The inner radius is:

  8. 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. Where R is the distance from the axis of rotation to the outer curve and r is the distance from the axis of rotation to the inner curve.

  9. The washer method formula is: r R Where R is the distance from the axis of rotation to the outer curve and r is the distance from the axis of rotation to the inner curve. Since the region being rotated is one bound by two curves, could we also consider R to be the upper curve and r to be the lower curve?

  10. Find the volume of the region bounded by , , and revolved about the y-axis. We can use the washer method if we split it into two parts: First, the cylinder on the bottom Everything above that will require washers… Cylinder inner radius outer radius thickness of slice

  11. Cylinder inner radius outer radius thickness of slice p

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