 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
Question from Bryan, a student: How many cubic yards of aggregate must be ordered for a road base 16 in. thick and 2 miles long with a top width of 30 ft, if the side slopes are one on one, or 45 degrees |
Hi Bryan.
The area of the cross section times the length of the road base will give you the volume needed.
The cross section is a trapezoid (the top and bottom are parallel lines). The area of a trapezoid is (1/2)(h)(a+b) where h is the height between the parallel sides, and a and b are the lengths of the parallel
sides. If a is the top, then it is just 30 ft.
You'll need to calculate the length of the bottom of the road base. To do that, remember that a 45 degree angle means that the length extensions (on each side), the slope and the depth form a right isosceles triangle, so the length extension is the same as the depth.
Hope this helps. Keep your units straight!
Stephen La Rocque
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.