The circumference of a sphere was measured to be 86 cm with a possible error of 0.2cm.
Use differentials to estimate the maximum error in the calculated surface area. Please round the answer to the nearest tenth.
What is the relative error in the calculated surface area? Please round the answer to the nearest tenth.
_________%
Use differentials to estimate the maximum error in the calculated volume. Please round the answer to the nearest tenth.
What is the relative error in the calculated volume? Please round the answer to the nearest tenth.
%
For small deviations, the relative area error is twice the relative length (radius or circumference) area, and the relative volume error is three times the relative length error.
In your case the relative length error is 0.2/86 = 0.233%
The relative area error (rounded to 0.1%) is therefore 0.4% and the relative volume error is 0.7%
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