Consider a cone with base radius $r$ and vertical height $h = r$. A sphere also has radius $r$. What is the ratio of the volume of this specific cone to the volume of the sphere?

True or False: If a sphere has a volume of $V$, then the volume of the smallest cylinder that can circumscribe it is exactly $\frac{3}{2}V$.

Based on the geometric relationship attributed to Archimedes, the volume of a sphere is exactly what fraction of the volume of the cylinder that just fits around it (the circumscribed cylinder)?

True or False: If a sphere has a radius $r$, the volume of the 'tightest' cylinder that can hold it (the circumscribed cylinder) is given by the formula $V = 2\pi r^3$.

Archimedes established that the volume of a sphere is two-thirds the volume of its circumscribed cylinder. If the cylinder that perfectly encloses a sphere has a volume of $30\pi\text{ cm}^3$, what is the volume of the sphere?