How could I find the volume of this equation (x^2+y^2+z^2+12)^2=64(x^2+y^2) using triple integrals in both spherical and cylindrical coords ? Thank you !

Hi, I have an homework where I need to find the highest point and the lowest point on an ellipse form by the intersection of two equations wich are 4x-3y+8z=5 and z^2=x^2+y^2 and I have to use the LagrangeMultiplier command. I get how it works but I can't get the correct form. How should I do it ?