A couple of methods given below for estimating the volume of the big yellow bag -- and the logic for the final volume.
Final volume estimate = 53.4 cubic feet -- I think this is likely accurate within plus/minus 2 %.
Approximate as a cylindrical section with domes on each end.
volume of constant section cylinder:
Length of cylinder = 61 inches
Diameter of cylinder = (measured circumference)/Pi = 123.75 / Pi = 39.4 inches
Volume of Cylinder = (d^2)*(Pi/4)*L = 39.4^2*0.785* 61 = 74335 cubic inches
Volume of dome ends:
Height of dome = 11.5 inches
Diameter of dome where it joins the cylinder = 39.4 inches.
From this Wikipedia page: http://en.wikipedia.org/wiki/Dome_%28mathematics%29
Rc = (11.5^2 + (d/2)^2 ) / (2*11.5) = 22.6 inches
Volume dome = Pi*22.6*11.5^2 = 0.333*Pi*11.5^3 = 7799 cubic inches
Total volume = Cylinder Volume + Right end dome + Left end dome = 74335 + 7799 + 7799 = 89932 cubic inches = 52 cubic feet
If done as an oblate elipsoid, the volume of a dome end would be:
Volume = (4/3)*(Pi)*(a)*(b)*(c)
Where a and b are the equatorial radi -- a = b = 39.4/2 = 19.7 inches
c is the polar radius = 11.5 inches
Volume = 1.33*Pi*19.7*19.7*11.5 = 18648 cubic inches for the full ellipsoid, or 9324 cubic inches for each dome end.
I think the ellipsoid ends are probably more accurate in that they some in tangent to the cylinderical wall section.
So, section of spere dome = 7799 and ellipsoidal come = 9324 --- use 9000 cubic inches for each dome end.
Total volume = Cylinder Volume + Right end dome + Left end dome = 74335 + 9000 + 9000 = 92335 cubic inches = 53.4 cubic feet
