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Solutions for Session 6, Part A
See solutions for Problems: A1 | A2 | A3 | A4 | A5 | A6
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Problem A1 | |
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No, the surface area should be identical, since it is the fingers, not their location, that determine the area. The same shapes in different locations will have the same area.
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Problem A2 | |
a. | A good unit of measurement might be a square centimeter or a square millimeter on grid paper. An important aspect is that the unit should tile well. |
b. | A circle does not tile well; circles leave holes in between them, and counting the area of the circles would not approximate the total area of the hand. |
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Problem A3 | |
a. | Answers will vary. Counting squares is subject to several errors, including the possibility of miscounting the squares and the rounding error introduced by trying to count "half squares." Additionally, it may not be the most precise method. It also takes a while to do. |
b. | Answers will vary. Using two different methods will most likely result in different numerical values, since the area in both cases is an approximation and therefore subject to error. |
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Problem A4 | |
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Answers will vary. One useful method is to use paper with a finer grid, as smaller squares (units) will result in fewer rounding errors.
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Problem A5 | |
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This is a reasonable method of approximation, although there are still other forms of measurement error that can have an effect on the calculation. We can increase the accuracy of our measurement by making the units smaller, for example, using mm2 instead of cm2 grid paper. But because we are physically measuring it, the area will always be an approximation, no matter how small the unit (and there's always a smaller unit!). The measurement process always results in an approximate rather than an exact value.
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Problem A6 | |
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Answers will vary. You can make this approximation by multiplying your palm's area by 100.
<< back to Problem A6
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