Chapter 5.6, Problem 354E

[T] The average density of a solid Q is defined as Pave = ${\rho }_{ave}=\frac{1}{V\left(Q\right)}{\displaystyle \underset{Q}{\iiint }\rho \left(x,y,z\right)dV}=\frac{m}{V\left(Q\right)}$ , where V(Q) and m are the volume and the mass of Q. respectively. If the density of tile unit ball centered at tile origin is $\rho \left(x,y,z\right)=e^{-x^2-y^2-z^2}$use a CAS to find its average density. Round your answer to three decimal places.