Describe what happens to the surface area to volume ratio for larger and larger cubes. Predict if this pattern would also be observed for other geometric shapes such as a sphere. Explain the reasoning behind the prediction.
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Tena Star
ANSWERS: 1
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Surface area for a cube of side a: 6 a^2 Volume = a^3 ratio = a/6 which increases linearly with a. This is observed for ALL geometric shapes. If you multiply the size of the shape by k, then all lengths go up by a factor of k. In particular, the size of the sides on any square area on the surface of the shape will go up by a factor of k, and the area will go up by a factor of k*k. Similarly any cubic volume inside the shape will increase by k*k*k times. You can approximate the area and volume as accurately as you like with square and cubic bits, so the whole shape does the same thing.
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