Half a Sphere

A hemisphere is half a sphere, so it holds half a sphere's volume. Half of 4/3 is 2/3.

This bowl has radius 6, so ${r}^{3} = 216$. Its volume is $\frac{2}{3}\cdot \pi\cdot 216 = 144\cdot \pi$. The whole ball of radius 6 would hold twice that, 288π.

The rule is Volume of a hemisphere: $V = \frac{2}{3}\cdot \pi\cdot {r}^{3}$. The radius is still cubed, and the result is always exactly half the sphere's.