Question 144116
Imagine the curved surface of the actual bed of the dump truck as one-fourth of an imaginary cylinder with radius r = the radius of curvature at the bottom of the truck bed.  Now imagine a rectangular solid with a square base with sides = the diameter of the previously described cylinder.  The cylinder comprises approximately 78.54% of the volume of the rectangular solid, therefore the 4 pieces of the rectangular solid NOT part of the cylinder comprise about 21.46% of the rectangular solid.  It is one of those 4 pieces whose volume you seek, so, divide 21.46 by 4 = 5.36% (approx).  Multiply the radius of curvature by 2, square the result, multiply by the length of the bed, and then multiply the result by .0536.  Do this for each of the three curved corners (five if you count the vertical corners) of the bed of the truck, and add up the results.  Subtract this value from the calculated volume of a notional truck with perfectly square corners in the bed.