Finding volume of a cone given densityLet C be the solid cone with the boundary surfaces x 2 + y 2 = z 2 and z = 0. The density of the solid at point (x,y,z) is z.Find the volume of the solid using the integrals in both the cylindrical coordinates and the spherical coordinates.I really cant do this question. I know that V = ρ / m but what is m?I also don't understand how you can even find the volume with integrals because there is no limit of z given so it would just be infinity wouldn't it.Can someone start me off, I obviously don't need anyone to show me how to integrate. Just struggling on what the density and stuff is relevant.

Question

Finding volume of a cone given densityLet C be the solid cone with the boundary surfaces       x    2    +      y    2    =      z    2   and   z  =  0. The density of the solid at point (x,y,z) is z.Find the volume of the solid using the integrals in both the cylindrical coordinates and the spherical coordinates.I really cant do this question. I know that   V  =  ρ      /    m but what is m?I also don&#039;t understand how you can even find the volume with integrals because there is no limit of z given so it would just be infinity wouldn&#039;t it.Can someone start me off, I obviously don&#039;t need anyone to show me how to integrate. Just struggling on what the density and stuff is relevant.

Szulikto · Accepted Answer

Explanation:As a start cylindrical coordinates case is simpler perhaps by cylinders stacking summation   d  V  =  ρ  π      r    2    d  z  ρ  =  z  ,  r  =  z  V  =  π  ∫      z    3    d  z  =      z    4    π      /    4 etc...

Let C be the solid cone with the boundary surfaces x^{2}+y^{2}=z^{2} and z=0. The density of the solid at point (x,y,z) is z.

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