Penny Problem Lab Report

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Challenge #1 — The Penny Problem: The volume of a cylinder is V=πr2h. Since the pennies and the container both are cylinders we can apply that formula with the information we have. To find the volume of the pennies I took v=πr2h --> v=(3.14)(0.3752)(0.061) --> v=0.02693. Then to find the volume of the container, I took v=πr2h --> v=(3.14)(32)(11.5) --> v=(3.14)(9)(11.5) --> v=324.99. Now that I have the volume of the pennies and the container, I can divide them and get how many pennies can fit in the jar. 324.99/0.02693=12,067.95 approximatly 12,068 pennies can fit into the jar. Challenge #2 — Tennis Trouble: The volume of the tennis balls can be found using V=4/3πr3. To find the volume I just use the formula and the information I'm given:…show more content…
For the Penny Problem, how much empty space should exist inside the jar after being filled to capacity with pennies? The amount of empty space inside the jar after being filled to capacity with pennies is about .5. 2. Where does the formula for the volume of a cylinder derive from? Give an example, and provide evidence to support your claim. The formula for the volume of a cylinder derives from the area formula of a…show more content…
In the Tennis Challenge, a cone was used for calculations, and in Giant Gum, the formula for the volume of a pyramid was needed. Pick either the formula for the volume of a cone or the volume of a pyramid, and explain where the formula you chose derives from? The formula I pick is the formula of a cone. The formula of a cone derives from the volume of a cylinder. 4. If the container’s shape was modified to look like container "B," what effect would it have on the capacity (volume) of the container if the dimensions remained unchanged? What theory or principle helps to prove your point? If the dimensions remained unchanged, then that means the volume will stay the same. The principal that helps prove my point is Cavalieri's principal. 5. In Giant Gum, the gum is shaped like a pyramid. What shape do you think would best fit into the container? (Choose a shape other than a pyramid.) Explain why the shape you chose was better and back up your answer with proof, such as calculations and writing. The shape I think woud fit the best in the container is a sphere obviously, just because it was a sphere shaped container. I think more would fit inside the container that way. The volume would be easier to find considering you have the same formula for both the gum and the
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