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Home Newtonian Physics Scaling and OrderofMagnitude Estimates Examples Scaling of the volume of a sphere  
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Scaling of the volume of a sphere
In figure n, the larger sphere has a radius that is five times greater. How many times greater is its volume? Correct solution #1: Volume scales like the third power of the linear size, so the larger sphere has a volume that is 125 times greater (5^{3} = 125). Correct solution #2: The volume of a sphere is V = (4/3)πr^{3}, so
Incorrect solution: The volume of a sphere is V = pr^{3}, so
(The solution is incorrect because (5r_{1})^{3} is not the same as 5r^{3} _{1}.)


Home Newtonian Physics Scaling and OrderofMagnitude Estimates Examples Scaling of the volume of a sphere 