Kiwonghsmfa

We want the surface area of the portion of the cone z^2 = x^2 y^2 between z=0 and z=8 The equation of the cone in cylindrical coordinates is just z = r, so we can take as our parameters r and t (representing theta) ***** treat that potion(S) of the cone as a graph whose shadow D on the xyplane is the disk of radius 8 The Sphere is x² y² z² = 1 And cone z = 6√(x² y²) The volume of the Sphere is Where x,y and z are in Cartesian coordinates and Ѳ, φ and ρ are in Spherical coordinate systemLast, in rectangular coordinates, elliptic cones are quadric surfaces and can be represented by equations of the form z 2 = x 2 a 2 y 2 b 2 z 2 = x 2 a 2 y 2 b 2 In this case, we could choose any of the three However, the equation for the surface is more complicated in rectangular coordinates than in the other two systems, so we might X 2 Y 2 Z 2 4 Spherical Coordinates Graph of cone z=sqrt(x^2 y^2)