This came from an engineering board exam and I can't solve it. Find approximately the difference between the areas of two spheres whose radii area 4 ft. and 4.05 ft.
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The surface area of a sphere is $\displaystyle S=4\pi r^2$. I'm guessing that the problem wants you to use differentials to get the approximation. $\displaystyle dS = 8\pi rdr = 8\pi (4)(.05) = 1.6\pi$.
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