It's a complete disaster! I just don't get it.
1)
Quote: "Exactly 1 mm of precipitations fall down on the pitch each minute"
Another quote: "You should output the average amount of precipitations (in millimeters) falling on the pitch in a minute."

So the reasonable question is: "Why the answer is just the area of the pitch without a small piece??" It shoud be less than one millimeter!
Ammount of precipitations is the height of the water column that arises from the surface in a particular period of time. Hence under the umbrellas the ammount equals to zero. And according to the statement the answer is (1 - area_covered_with_umbrellas / area_of_the_pitch).

2)
Quote: "All the water that has fallen on an umbrella streams down along the shortest way on the hemisphere."

So what? Does it mean that the water from the umbrella falls back on the pitch without changing the answer? Or, may be, it changes somehow the ammount of precipitations in the area near the umbrella... And if the umbrella is on the border of the pitch, than what ammount of water falls outside the pitch - area of spherical sector or area of its projection or area of spherical sector minus area of the layer falling out of the pitch?
BTW None of these variants didn't produce the answer given in the sample output.

I'd appreciate any information you could give me to remove an ambiguity.

1)HINT: за счёт зонтов осадков может выпасть больше.

2)"Вся вода попавшая на зонт, стекает по радиусам зонта от центра к краям" и затем падает вертикально вниз.