A firecracker explodes at a height of $100\mathrm{m}$ 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 $20\mathrm{m}/\mathrm{s}$.

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

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