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Solutions for Session 9 Homework
See solutions for Problems: H1 | H2 | H3 | H4 | H5
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Problem H1 | |
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Dinosaurs' plates were likely the result of their very low surface area-to-volume ratio: The plates served to increase the dinosaurs' surface area without increasing their volume very much.
Animals with a great deal of surface area but little volume cool down and heat up faster than animals with larger volumes. This is important in reptiles since they obtain their body heat from the sun.
<< back to Problem H1
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Problem H2 | |
a. | The minimum surface area occurs when the height is exactly twice the radius. If the volume is 500 cm3, the radius is approximately 4.30 cm, while the height is approximately 8.61 cm. |
b. | In this shape, the can fits perfectly inside a cube, since the diameter of the can is the same as the height. Some cans are made in this shape. When cans are displayed in stores or placed on shelves, there is often more of a premium on radius (shelf space), so the radius is often smaller than our "ideal" can. |
<< back to Problem H2
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Problem H3 | |
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One obvious way is to increase the surface area-to-volume ratio of the tablet. It would dissolve more quickly. A flat caplet dissolves more quickly than a spherical pill.
<< back to Problem H3
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Problem H4 | |
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This is the same type of problem as the "area of the hand" problem in Problem A7. The answer depends on the shape of the rectangle Mr. Hobbs used, since different rectangles with the same perimeter will have different areas. There is no way of guaranteeing that, using this method, the area of the two figures would be the same.
<< back to Problem H4
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Problem H5 | |
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Yes, a similar ratio exists. The ratio for spheres is r:3 rather than s:6 for cubes and can most easily be found by using a table or by dividing the two formulas into one another.
<< back to Problem H5
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