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You're using the same ratio of mile/px as the accepted calc, except it has clear differences, such as: Your line being massively bigger then the one used in the original calc. Another thing is that you can't use the same mile/px ratio using a completely different map. Even if it is the same image, you still need to draw the pixel lines and measure them because there might be a difference: The map you grabbed might be different or, your own monitor might be bigger/smaller, causing the mile/pixel ratio to be wrong, so you need to redo the pixel scaling one way or the other (I would personally recommend grabbing the map with the mile/px ratio and do it there, but still resizing the line over there to make sure the mile/px ratio is the same for you)
And this next part is not something wrong, but try to be more concise with your convertions. If you did something in miles, the result should be in miles³, you put the end result as meters³, but you didn't even used it and instead just converted the vallue to centimeter³ "off screen". I would recomment you either giving the result as miles³, then converting it cm³ (You can just do something like "X mi³, which is the same as Y cm³" or just convert the miles into cm and do the volume using cm