CRMS Calculus 2010 May 21, 2010
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CRMS Calculus 2010 May 21, 2010

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Calculating volumes by plane slicing

Calculating volumes by plane slicing

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CRMS Calculus 2010 May 21, 2010 CRMS Calculus 2010 May 21, 2010 Presentation Transcript

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  • Generating Solids of Revolution Using play­doh, and a skewer as the axis of rotation, build the solid generated when the indicated  plane region is revolved about the given line. 2
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  • Calculating Volumes From Flickr by williewonker 4
  • Calculate the volume of the following items, with the given restriction. 1. Deck of playing cards. You may only measure one card. Find volume of one card by, finding cross­sectional area of one card, multiplied by thickness of the card. Count number of cards (52). Multiply volume of one card by a52. 2. A roll of pennies. You may only measure one penny. Volume of one penny = Cross­sectional area (circle = ∏r2) times thickness of penny. Count number of pennies in roll. Multiply volume of one penny times number of pennies in roll. 3. A rectangular loaf of bread. You may only measure one slice of bread. Find volume of one slice of bread by, finding cross­sectional area of slice (A = bh), multiplied by thickness of the slice of bread. Count number of slices of bread in the loaf. Multiply volume of one slice by number of slices in loaf. 4. A circular cylinder of rice cakes. You may only measure one rice cake. Volume of one rice cake = Cross­sectional area (circle = ∏r2) times thickness of cake. Count number of rice cakes in package Multiply volume of one rice cake by number of rice cakes in package. ***  Each item above had a cross­sectional area that was ____________________. What if you were asked to find the volume of a solid with a variable cross­sectional area. 5. ________________________, with n slices of with equal thickness.  .................. Sounds like a job for .......... 5
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