Hello all you math lovers out there! So I am no longer in gr. 10 and sadly am not doing really super, hard math anymore but I thought I would go through the calculations for the math project I just handed in today :D There are a few things that you need to know but I'm too tired to fully explain, so it's going to be as simple as I can make it. I'll begin with diagrams, as I know everyone loves diagrams :)
Figure 1 - a top view of the pond area that you are trying to fill, the depths of each of the dots are given in the question.
Figure 2 - profile of the river that will be used to fill the pond, each depth is given in the question.
.
Figure 3 - table of the depths, etc of the pond in Figure 1
The project was to find out how long it took for a pond to fill with only rainwater, how long it would take to fill the pond if a nearby creek was diverted to the pond and the total volume of the pond. Figure 3 shows the first table I set up in excel to determine the volume of the pond.
I was giving the depths of the pond in different points across the pond and with that you use either the Trapezoid rule or the Simpson's rule .
Using either the Simpson's or the Trapezoid rule you can determine the surface area of each of the cross sections of the pond. Then with all those areas you can use the Simpson's rule again to determine the volume of the pond! I set my excel spreadsheet up like this.