Answer:
mass = 9a^5
center of mass = [tex]\frac{7a}{12}, \frac{7a}{12}, \frac{7a}{12}[/tex]
Step-by-step explanation:
Finding the mass of the solid E
given density function : p ( x,y,z ) = [tex]9x^2 + 9y^2 + 9z^2[/tex]
Mass = [tex]\int\limits^a_0 \int\limits^a_0 \int\limits^a_0 {9(x^2+y^2+z^2)} \, dx dydz[/tex] [tex]= \int\limits^a_0 \int\limits^a_0 {9(\frac{a^3}{3}+ay^2+az^2 )} \, dydz[/tex]
[tex]= \int\limits^a_0 {9(\frac{a^4}{3}+\frac{a^4}{3} +a^2z^2 )} \, dz[/tex] [tex]= \int\limits^a_0 {9(\frac{2a^4}{3}+a^2z^2 )} \, dz[/tex] [tex]= 9 ( \frac{2a^5}{3} + \frac{a^5}{3} )[/tex]
( taking limits as a and 0 )
hence Mass = 9 [tex](a^5)[/tex]
finding the center of mass
attached below is solution
