This is a very interesting topic. This problem seems simple, but in fact it needs serious consideration.
First of all, what is a "common part" must be clearly distinguished: the "common part" of two cylinders (see the left figure below) and the "common part" of the third cylinder are different from the "common part" of two intersecting cylinders (see the right figure below).
Assuming that the volumes of the above two "commonly used * * * parts" are V2 (bottom left) and V3 (bottom right) respectively, the required volume =2*2*2-(3*2*π/4-V2-V3).
Let's use the integral method to calculate V2 and V3 (no better method can be found):
To facilitate the calculation, the actual volume is calculated by enlarging the coordinates by 2 times and then reducing the calculated volume by 8 times:
V2=[8∫( 1，0)∫(√( 1-x*x)，0)
√( 1-y*y)dydx]/8=2/3
V3=[ 16∫( 1， 1/√2)√( √( 1-x * x)，0)
√( 1-y*y)dydx
+ 16∫( 1/√2，0)∫(x，0)
√( 1-y*y)dydx]/8=√2-2/3
So the volume = 2 * 2 * 2-(3 * 2 * π/4-V2-V3) = 8-3 * π/2+√ 2 √ 4.7 (cubic centimeter).