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Volumes

Volumes. Right Cylinder. Volume of a Right Cylinder (Slices). Cross section is a right circular cylinder with volume . Also obtained as a solid of revolution. Consider the case when h=5 and r=2. Volume of a Rectangular Box. Area of a cross section is b*l.

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Volumes

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  1. Volumes

  2. Right Cylinder

  3. Volume of a Right Cylinder (Slices) Cross section is a right circular cylinder with volume Also obtained as a solid of revolution Consider the case when h=5 and r=2

  4. Volume of a Rectangular Box Area of a cross section is b*l Cross section is a right cylinder with volume Consider the case of a box with dimensions 3x5x7

  5. Volume of a Sphere of radius r (slices) Cross section is a right cylinder with volume Consider the case of a sphere of radius r=3

  6. Another Example Sketch the solid of revolution obtained by rotating around x-axis and find its volume Sketch the solid of revolution obtained by rotating around y-axis and find its volume Sketch the solid of revolution obtained by rotating around x=5 and find its volume

  7. Volume using Shells

  8. Example Sketch the solid of revolution obtained by rotating about x-axis and find its volume Sketch the solid of revolution obtained by rotating around y-axis and find its volume Sketch the solid of revolution obtained by rotating around x=1.2 and find its volume

  9. Cylindrical Shells • Definition of a shell • Animations

  10. Formulas • Shell in general position Volume of shell

  11. Volume Formulas Function y=f(x) • Rotating about y-axis • Function x=f(y) • Rotating about x-axis

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