c) Evaluate the following triple integral in spherical coordinate system !!! 2² x² + y² + 2² dV where G is the solid bounded above by spheres, p = 4 and below by x² + y² p= 2 in the cone, z = 3

dont submit handwritten

By transforming into spherical polar coordinates, evaluate |[ dxdydz V1-x²-y2-z2 taken throughout the -z' volume contained in the positive octant of the sphere 2. 2. x² +y² + z² = 1.

Please don't provide handwritten solution ....

Q1) Consider a uniform solid rectangular block of mass m and dimension 2ax2b×2c. Find the equation of the momental ellipsoid for a corner O of the block, referred to the edges through O as co-ordinates axes and hence determine M.I. about OP, where P is the point diagonally opposite to O

a) The equation of the unit sphere of three-dimensional space is X²+Y²+Z² = 1. The variables are stretched by coefficients a, b and c: x = ax, y = bY and z = cZ. What is the relationship between the new variables x, y and z? What is the name of this surface? b) Form the parametrization of the surface at point a by stretching the parametrization of the sphere in a suitable way. c) Determine the surface related to the previous points 3x² + 4y² + 5z² = 33 normal vector at a point (2, −2, 1).