?[T] The average density of a solid Q is defined as \(\rho_{\text {ave }}=\frac{1}{V(Q)}
Chapter 5, Problem 354(choose chapter or problem)
[T] The average density of a solid Q is defined as \(\rho_{\text {ave }}=\frac{1}{V(Q)} \iiint_{Q} \rho(x, y, z) d V=\frac{m}{V(Q)}\) , where V(Q) and m are the volume and the mass of Q, respectively. If the density of the unit ball centered at the origin is \(\rho(x, y, z)=e^{-x^{2}-y^{2}-z^{2}}\) , use a CAS to find its average density. Round your answer to three decimal places.
Text Transcription:
rho_ave = 1/V(Q) iiint_Q rho(x, y, z) dV = m/V(Q)
rho(x, y, z) = e^-x^2 - y^2 - z^2
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