The radius of a spherical balloon is measured as 8 inches, with a possible error of 0.02 inch. (a) Use differentials to approximate the possible propagated error in computing the volume of the sphere. (b) Use differentials to approximate the possible propagated error in computing the surface area of the sphere. (c) Approximate the percent errors in parts (a) and (b).

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The radius of a spherical balloon is measured as 8 inches, with a possible error of 0.02 inch. (a) Use differentials to approximate the possible propagated error in computing the volume of the sphere. (b) Use differentials to approximate the possible propagated error in computing the surface area of the sphere. (c) Approximate the percent errors in parts (a) and (b).

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