Simple Unit Conversion Word Problem Help

[opus]

Homework Statement

During a heavy rain, a section of mountainside measuring 2.5 km horizontally, 0.80 km up along the slope, and 2.0 m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 0.40km x 0.40km and that mud has a density of $\frac{1900~kg}{m^3}$. What is the mass of the mud sitting above a 4.0 $m^2$ area of the valley floor.

Homework Equations

The Attempt at a Solution

Please see attached image so you can see how I am visualizing the problem.
My thought was to take the volume of the mud initially on the mountainside, and use that to determine how deep the mud is when it has moved to the valley. From this, I can get a specific volume of mud and use dimensional analysis to get a mass of the mud over the given area. My answer is way off the mark.

 

[TSny]

What is the mass of the mud sitting above a 4.0 $m^2$ area of the valley floor.

Note that the area 4.0 m² does not correspond to a square of side length 4.0 m. The area of such a square would be 16 m².

 

[opus]

Note that the area 4.0 m² does not correspond to a square of side length 4.0 m. The area of such a square would be 16 m².

Ah! That was a dumb mistake. So then the side lengths are each 2m, and my final answer is $1.9⋅10^5$ kg which matches with the back of the book. Thank you!

 

[TSny]

Looks good. Of course, you would still get the same answer even if the base area did not have the shape of a square. All that matters is that it have an area of 4.0 m².

 

[opus]

I'll keep that in mind. Been doing a lot of these to prepare for the start of the semester on Monday, so I appreciate the response at this time of night.