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Area, Volume, and Arc Length
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Calculus
Area, Volume, and Arc Length
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Area, Volume, and Arc Length Exercises
Area
We need to learn to slice flat food first. After it is has been de-boned, a fish such as salmon is relatively flat.We are going to make fish sticks, so we need to cut it into thin strips. We slice...
Integrating with Polar Coordinates
Slicing Cold PizzaFirst, let's forget about calculus and use our knowledge of fractions to answer the following question.Sample ProblemWhat is the area of the shaded region?Answer.Think of the shad...
Volumes of Solids with Known Cross-Sections
We already mentioned that slicing a solid with known cross-section is like slicing a loaf of cinnamon raisin bread. We could also think of it like we are slicing carrots for pot roast or potato sli...
Pyramids, Cones, and Spheres
Welcome to the jungle. We won't find any scrumptious sweets here, unless our jungle is in the middle of Oz. Our well-being depends on us being able to tackle finding volumes of more complicated obj...
Volume of Solids of Revolution
Solids of revolution are not fruits thrown at tyrannical rulers in protest. A solids of revolution is a volume built by rotating an area around a predetermined center line called the axis of rotati...
Arc Length
We've prepared our fish by cutting it into flat rectangular portions and we've sliced our vegetables into thin slices. We've even gone off on a tangent, playing with frisbees and toilet paper tubes...