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# (Solved): Why does distance between point and z-axis being propritonate make the density function k(sqrt(x^2 ...

Why does distance between point and z-axis being propritonate make the density function k(sqrt(x^2+y^2))?

Use spherical coordinates to find the mass of the sphere $$x^{2}+y^{2}+z^{2}=a^{2}$$ with the given density. The density at any point is proportional to the distance of the point from the $$z$$-axis. Step-by-step solution Show all steps [3 $$75 \%$$ (12 ratings) for this solution Step 1/3 Consider the following sphere: $x^{2}+y^{2}+z^{2}=a^{2}$ The objective is to find the mass of the sphere, using spherical coordinates. The spherical coordinates are, $x=\rho \sin \phi \cos \theta, y=\rho \sin \phi \sin \theta, z=\rho \cos \phi$ The density at any point is proportional to its distance from the z - axis. The density function is, $\begin{array}{r} \rho(x, y, z) \alpha \sqrt{x^{2}+y^{2}} \\ \rho(x, y, z)=k\left(\sqrt{x^{2}+y^{2}}\right) \end{array}$

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