8. A hot-air balloon has the truncated spherical shape. The hot gases escape through the porous envelope with a velocity vector ?eld V (z, y, z) = â½ Ãé(z, y, z) whereé(z, y, z) = +zj If R 2, compute the volume ?ow rate of the gases through the surface. (Use symbolic notation and fractions where needed.) Use Stokes' Theorem to convert the surface integral calculation into one involving a line integral whose region of integration corresponds to the curve where the hot-air balloon was truncated
Show transcribed image text8. A hot-air balloon has the truncated spherical shape. The hot gases escape through the porous envelope with a velocity vector ?eld V (z, y, z) = â½ Ãé(z, y, z) whereé(z, y, z) = +zj If R 2, compute the volume ?ow rate of the gases through the surface. (Use symbolic notation and fractions where needed.) Use Stokes' Theorem to convert the surface integral calculation into one involving a line integral whose region of integration corresponds to the curve where the hot-air balloon was truncated