Volume of sand of a slope inside a circle

[imprisonedpride]

Hello friends. I need to order sand to put under a pool. The pool is 18' wide, and it is recommended to add a slope (triangle) of sand 3" tall, 8" wide, around the entire inside of the pool to help the liner bend to the bottom, instead of making it turn 90 degrees on the ground:



Imagine the red section goes completely around the inside of the pool, like a funnel. I can calculate the area of the triangle, and the area of the 8" donut, but I don't know how to translate that to volume and go all the way along the inside of the 18' pool. Does anyone know the way to figure out this volume?

Thanks. M.

 

[stapel]

I need to order sand to put under a pool. The pool is 18' wide, and it is recommended to add a slope (triangle) of sand 3" tall, 8" wide, around the entire inside of the pool to help the liner bend to the bottom, instead of making it turn 90 degrees on the ground:

View attachment 35680

Imagine the red section goes completely around the inside of the pool, like a funnel. I can calculate the area of the triangle, and the area of the 8" donut, but I don't know how to translate that to volume and go all the way along the inside of the 18' pool. Does anyone know the way to figure out this volume?

This sounds like a "volume of a solid of revolution" calculus exercise. Set up the expression for the cross-sectional area. Then do the rotation.

(Note: The volunteers on this site help students struggling with math. We aren't contractors.)

Eliz.

 

[Dr.Peterson]

Hello friends. I need to order sand to put under a pool. The pool is 18' wide, and it is recommended to add a slope (triangle) of sand 3" tall, 8" wide, around the entire inside of the pool to help the liner bend to the bottom, instead of making it turn 90 degrees on the ground:

View attachment 35680

Imagine the red section goes completely around the inside of the pool, like a funnel. I can calculate the area of the triangle, and the area of the 8" donut, but I don't know how to translate that to volume and go all the way along the inside of the 18' pool. Does anyone know the way to figure out this volume?

Thanks. M.

For a quick approximation (which should be pretty good), just think of it as being straightened out to make a triangular prism with the "base" shown, and "height" (length) equal to the circumference of the pool. (Pappus' centroid theorem tells you how to change this into an exact solution, but you don't need that.)