View
807
Download
1
Embed Size (px)
DESCRIPTION
Calculating volumes by plane slicing
Citation preview
1
2
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.
3
4
From Flickr by williewonker
Calculating Volumes
5
Calculate the volume of the following items, with the given restriction.
1. Deck of playing cards. You may only measure one card.
2. A roll of pennies. You may only measure one penny.
3. A rectangular loaf of bread. You may only measure one slice of bread.
4. A circular cylinder of rice cakes. You may only measure one rice cake.
*** 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 ..........
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.
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.
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.
Volume of one rice cake = Crosssectional area (circle = ∏r2) times thickness of cake.Count number of rice cakes in packageMultiply volume of one rice cake by number of rice cakes in package.
6