Ένα κυλινδρικό βαρέλι με ακτίνα
![[asy]
import three; import solids;
size(5cm);
currentprojection=orthographic(1,-1/6,1/6);
draw(surface(revolution((0,0,0),(-2,-2*sqrt(3),0)--(-2,-2*sqrt(3),-10),Z,0,360)),white,nolight);
triple A =(8*sqrt(6)/3,0,8*sqrt(3)/3), B = (-4*sqrt(6)/3,4*sqrt(2),8*sqrt(3)/3), C = (-4*sqrt(6)/3,-4*sqrt(2),8*sqrt(3)/3), X = (0,0,-2*sqrt(2));
draw(X--X+A--X+A+B--X+A+B+C);
draw(X--X+B--X+A+B);
draw(X--X+C--X+A+C--X+A+B+C);
draw(X+A--X+A+C);
draw(X+C--X+C+B--X+A+B+C,linetype("2 4"));
draw(X+B--X+C+B,linetype("2 4"));
draw(surface(revolution((0,0,0),(-2,-2*sqrt(3),0)--(-2,-2*sqrt(3),-10),Z,0,240)),white,nolight);
draw((-2,-2*sqrt(3),0)..(4,0,0)..(-2,2*sqrt(3),0));
draw((-4*cos(atan(5)),-4*sin(atan(5)),0)--(-4*cos(atan(5)),-4*sin(atan(5)),-10)..(4,0,-10)..(4*cos(atan(5)),4*sin(atan(5)),-10)--(4*cos(atan(5)),4*sin(atan(5)),0));
draw((-2,-2*sqrt(3),0)..(-4,0,0)..(-2,2*sqrt(3),0),linetype("2 4"));
[/asy]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_satS4r8hngf_tbHvN_nPjydxzIgFDJw2WwcBx7-zGbFrVzbSN0uIAo6im3kNkhs8omHtJvkyOS2fvCSMpfoeu5bRSBgGBZz128-zxtPzUcT46iTYsmHscxJozeHlsqLTOc5KLPBiV4b4QNe6smmcZe0gaiXyWu5HKf=s0-d)
Να βρεθεί ο όγκος του εκτοπισμένου νερού.
AIME 2015
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