141. If $D$ is the diameter of a sphere, then $\frac{D^{3}}{2}+\frac{1}{21} \cdot \frac{D^{3}}{2}$ is the measure of the volume of the sphere. Determine the value of $\pi$ for which this statement is true.
141. We have $\frac{D^{3}}{2}+\frac{1}{21} \cdot \frac{D^{3}}{2}=\frac{\pi D^{3}}{6}$, or $\frac{\pi}{6}=\frac{1}{2}+\frac{1}{21} \cdot \frac{1}{2}$, from which

$$
\pi=3+\frac{1}{7}=\frac{22}{7}
$$