# Homework Help: Dredging bottom of river (3D Calculus)

1. May 25, 2010

### merzperson

I am given a contour map of the bottom of a river and I must determine how much material must be removed to make the river navigable.

Can someone help me by telling me how they'd go about solving this type of problem? My main problem is that I am not so sure what shape(s) to find the volume of.

Sorry I don't have this in the correct format, but the question is too general for such a format.

2. May 25, 2010

### Staff: Mentor

I assume the contour map is such that the water level is shown, and that the idea is to make the river some uniform depth. Is it also safe to assume that the river is relatively flat?

Suppose that at one stretch of the river there is a submerged island. The contour map will show this as concentric closed curves, with each curve at a particular depth, and each curve a certain depth above or below the curve next to it.

Overlay a grid of squares on the contour map, and for each contour level that isn't deep enough, approximate the area within the closed curve by counting the number of squares that are inside the curve, then multiply by the height differential between contours. The more squares in the grid, the better will be your approximation. Do that for as many contours as it takes to get down as far as you need.

If there's a hole in the river bottom, you can estimate the volume of the hole in the same way.

Does that give you any ideas?

3. May 25, 2010

### merzperson

Thank you Mark44! That was just what I needed to get started.