Example 8-3-4 - Maple Help



Chapter 8: Applications of Triple Integration



Section 8.3: First Moments



Example 8.3.4



 a) Obtain the centroid of $R$, the region that is bounded inside by the surface $\mathrm{ρ}=1+\mathrm{cos}\left(\mathrm{φ}\right)$ and outside by the sphere $\mathrm{ρ}=2$. (The variables $\left(\mathrm{ρ},\mathrm{φ},\mathrm{θ}\right)$ are spherical coordinates.)
 b) Impose the density $\mathrm{δ}\left(\mathrm{\rho },\mathrm{\phi },\mathrm{\theta }\right)={\mathrm{ρ}}^{2}$ on $R$ and find the resulting center of mass.

(See Example 8.1.14.)