(Solved): the diameter of a sphere The diameter of a sphere is measured to be \( 78 \mathrm{~cm} \) with a max ...

The diameter of a sphere is measured to be \( 78 \mathrm{~cm} \) with a maximum possible error of \( \pm 1 \mathrm{~cm} \). If we compute the volume of the sphere from this measurement, what is the maximum propagated error in this calculation? Round your answer to 4 decimal places. Recall: the volume of a sphere of radius \( r \) is \( V=\frac{4}{3} \pi r^{3} \) Error \( \approx \pm \) Hint: Carefully read what quantity was measured here. Express your previous rounded answer as a relative error. Round to 4 decimal places. Relative Error \( \approx \pm \) Express your previous rounded answer as a percent error. Note the percentage sign is already included. Percent Error \( \approx \pm \) \( \% \)