Problem H
Sphere
Input: standard input
Output: standard output
Time Limit: 2 seconds
Have
you watched the science fiction movie “Sphere”? In this movie there is an
sphere from outer space which enables a man to convert his night-mares into
reality. That is if you dream that you are being attacked by lion, in reality
your surrounding people will be attacked by lion. The problem is that the alien
people who sent the “Sphere” are now in earth. They have made an artificial
island to stay which is surrounded by unknown poisonous liquid. The scientists
of earth have failed to determine the chemical structure of this liquid but has
succeeded to determine one of its physical properties, the specific gravity (S.
G.). This S. G. of liquid changes with time. So our scientists measure the S.
G. every hour. The aliens don’t attack us. What they do is very simple, they
just release paired-spheres on the poisonous stream of liquid and these paired
spheres float towards human civilization and then materializes our night mares.
As these are paired spheres their destructive power is twice of the previous
sphere. The aliens are not good in physics and maths. So some of the paired
spheres created by them sinks in the poisonous liquid. As our scientists are
very good in physics we can determine the weight of the spheres but sadly they
are very week in mathematics. So they ask your help to determine the volume and
surface area of the paired sphere and also asks you to determine whether it
will float in the liquid or sink. You can be sure that the input values and
output specification will be such that you will not have to think about
precisions in case of sink and float. Consider pi=2*acos(0);
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Fig: A Paired Sphere (Though the
image looks like two circles actually they are two balls) |
Fig: A diagram of the given scenario |
The Input
First line of
the input file will be an integer N which indicates how many sets of inputs are
there. The next N line will contain N sets of input.
Each set (or
lines) contain five integers R1 (0<R1<=500) and R2 (0<R2<=500) (The
radius of the two spheres of the paired sphere in centimeter), d (The distance
between the centers of the two spheres in centimeter) and d>max(R1,R2)
and d<(R1+R2)), W the weight of the sphere
(W<10000000000) in grams and S(0<S<10) the specific gravity of the
poisonous liquid.
The Output
For each set of input there will be two lines of output.
The first line will be the volume of the sphere and the surface area of the
sphere (four digits after the decimal point) and the second line will be any of
the two according to the situation “The Paired-Sphere Sinks.” Or “The
Paired-Sphere Floats.”
Sample Input
210 10 15 300 1.0
20 20 30 650000 1.0
Sample Output
8017.6063 2199.1149The Paired-Sphere Floats.
64140.8500 8796.4594
The Paired-Sphere Sinks.
Shahriar Manzoor
“When you want to store a value in the range of 32 bit integer in a 16 bit integer variable,
it is very unlikely that the value will be stored properly and in many cases the
stored value will be negative. Similarly, if you expect that a blunt man
will evaluate your intelligence properly, you
are simply expecting too much.”