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Areas and Volumes

Areas and Volumes. Area of a circle. Area of a circle. Area of a circle. Area of a circle. We need a substitution. Find the limit points. Replace. Replace. Volume of a sphere. Area of ellipse- use parametric equations. The Rings of the Lord . r. w/2. R. The Rings of the Lord .

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Areas and Volumes

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  1. Areas and Volumes

  2. Area of a circle

  3. Area of a circle

  4. Area of a circle

  5. Area of a circle

  6. We need a substitution

  7. Find the limit points

  8. Replace

  9. Replace

  10. Volume of a sphere

  11. Area of ellipse- use parametric equations

  12. The Rings of the Lord r w/2 R

  13. The Rings of the Lord • Volume = r w/2 R

  14. Volume = r w/2 R

  15. Arc length

  16. Arc length

  17. You need a substitution

  18. You need a substitution

  19. A cable of length l is suspended between two towers of equal height a distance 2d apart, so that it sags a distance h in the centre. • The curve formed by a suspended rope or cable is called a catenary. Using a coordinate system with the lowest point of the catenary at the origin, it can be described by the equation • where a is a constant

  20. Use the arc length formula to show that

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