We consider a sphere with a circular pore embedded in an unbounded viscous fluid, where the rim of the pore moves in such a way that the radius of the sphere is constant. Away from the pore, the surface area stretches or compresses uniformly. An exact form for the axisymmetric velocity field which describes the quasi-static motion of the bulk fluid is calculated. The resulting dissipation function yields an analytical value for the aqueous drag coefficient for the sphere with a shrinking pore. Additionally, we examine the small hole and small angle limits, which converge to the unsteady flow for the expansion of a hole in a plane wall, and for the contraction of a circular disk.