Concept: Centre of Mass Positions

Body	CM Position	Measured From
Uniform rod (length L)	$L/2$	Either end
Uniform disc / ring	Geometric centre	—
Triangular lamina (height h)	$h/3$	Base
Semicircular ring (radius R)	$\dfrac{2R}{\pi} \approx 0.637R$	Centre of full circle
Semicircular disc (radius R)	$\dfrac{4R}{3\pi} \approx 0.424R$	Centre of full circle
Uniform solid hemisphere (radius R)	$\dfrac{3R}{8} = 0.375R$	Centre of flat face
Hollow hemispherical shell (radius R)	$R/2 = 0.5R$	Centre of flat face

Note the decreasing sequence of CM distances from the centre for curved shapes:

For any finite system: $\vec{r}_{cm} = \dfrac{\sum m_i \vec{r}_i}{M_{total}}$

For a body with a cavity: treat the cavity as a negative mass at the cavity's CM position.