Question

(a) find the volume of the solid that is enclosed by the cone z = px2 y2 and the sphere x2 y2 z2 = 2 using cylindrical coordinates. (b) repeat part (a) but using spherical coordinates.

Answer 1

The question involves finding the volume of a solid enclosed by a cone and a sphere using cylindrical and spherical coordinates, which requires correcting the provided equations and integrating in the respective coordinate systems.

Step-by-step explanation:

The question is asking for the volume of a solid enclosed by a cone and a sphere in both cylindrical and spherical coordinates. Since the provided information has some typos and lacks the precise definition of the cone, the formula for the cone should possibly be z = p \( \sqrt{x^2 + y^2} \), and the given equation of the sphere is also incorrect and should be x^2 + y^2 + z^2 = 2 for a sphere of radius \( \sqrt{2} \). In cylindrical coordinates, the volume can be found by integrating the height (z) of the cone from the base up to where it intersects with the sphere, using the radius as the variable of integration. In spherical coordinates, the volume can be found by integrating with respect to the radial distance and the angles.