|
Question 144116: What is the best way to determine the volume of the square-edged bottom corner of a material truck with rounded corners within the square corners? I am looking for the space between the square corner and the radius (times the length, naturally) divided by 27 to determine the take-out in cubic yards of a dump truck
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! 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.
|
|
|
| |
