Firecracker

A firecracker explodes at a height of 100 m above level ground. It breaks into a large number of very small fragments, which move in every direction; all of them have the same initial velocity of 20 m/s.

We assume that the fragments move without air resistance, in a uniform gravitational field with g=9.81 $m/s^2$.

Find the volume (in $m^3$) of the region through which the fragments move before reaching the ground. Give your answer rounded to four decimal places.