Calculating Volume of Earth Removed in Open-Pit Coal Mine

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Homework Help Overview

The problem involves calculating the volume of earth removed in an open-pit coal mine, specifically focusing on the conversion of land area measured in hectares to cubic kilometers based on a given depth.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the area conversion from hectares to square kilometers and the subsequent calculations for volume based on depth. There are attempts to clarify the correct conversion factors and the implications of these conversions on the final volume calculation.

Discussion Status

There is ongoing exploration of the correct conversion from hectares to square kilometers, with some participants providing hints and corrections regarding the calculations. Multiple interpretations of the conversion factors are being examined, and guidance has been offered to clarify the area measurements.

Contextual Notes

Participants are working under the constraints of the problem statement, which specifies the area and depth but does not provide additional context or information that might influence the calculations.

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Homework Statement




A unit of area, often used in measuring land areas, is the "hectare", defined as 104 m2. An open-pit coal mine consumes 80 hectares of land, down to a depth of 26 m, each year. What volume of earth, in cubic kilometers, is removed in this time?

Homework Equations





The Attempt at a Solution



I calculated the area to be a square, with each side being .8944(sqrt of 800,000 divided by 1000). I multiplied this by .026. It gave me .0232. Ths answer is not correct.
 
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Heres a hint:

I would start by figuring out how many kilometers squared there are per hectare, and then multiplying by 80. If you know that then you already have the top area converted to km. You seem like you know what you should do from there.
 
OK, there is .1km squared per hectacre. I multiplied by 80, then by .026. I got .208, which is not correct.
 
Your conversion from hectares to km^2 is incorrect. To figure out what is correct start with the equation 1,000,000 m^2 = 1 km^2. Then convert the 1 million m^2 to hectares, and then solve for how many km^2 are in one hectare.
 
lgen0290 said:
OK, there is .1km squared per hectacre.

this is not correct
 

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