Exercises - Volume

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• 1. Consider the finite region R bounded by the curves

  

  Find the volume of the solid obtained by revolving the region R about the x-axis.
  
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• 2. Consider the following region:

  

  Find the volume of the solid obtained by revolving the region R about the line y = −1.
  
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• 3. Consider the region R under the graph of the function

  

  Find the volume of the solid obtained by revolving the region R about the line x = −1.
  
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• 4. Consider the finite region R bounded by the curves

  

  Find the volume of the solid obtained by revolving the region R about the y-axis.
  
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• 5. Consider the finite region R bounded by the curves

  

  Find the volume of the solid obtained by revolving the region R about the line y = −1.
  
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  Answer
   

• 6. Find the volume of the ball with radius R with a cylindrical hole of radius r bored through its center:

  

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