If we are to find the volume, we solve for the function w(x,y,z). In this case, . Recall that when we find volumes in 3-space, we resort to a region in 2-space to determine the limits. In our case, we resort to a region in 3-space in order to find our limits. Then we can find the volume of the ball in 4-space.
Thus, it would make sense that (we need two triple integrals to take into consideration the two hemispheres of the ball).
From here, evaluate the integral. A simple change to spherical coordinates will do the job.
Can you continue? I hope my explanation makes sense...