## Firecracker

### Problem 317

Published on Saturday, 1st January 2011, 04:00 pm; Solved by 1512; Difficulty rating: 35%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.