Calculating Volume of Earth Removed in Open-Pit Coal Mine

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SUMMARY

The discussion focuses on calculating the volume of earth removed from an open-pit coal mine that spans 80 hectares and reaches a depth of 26 meters annually. The correct conversion from hectares to square kilometers is essential, with 1 hectare equating to 0.01 square kilometers. The volume calculation involves multiplying the area in square kilometers by the depth in kilometers, leading to the formula: Volume = Area (km²) × Depth (km). The final volume of earth removed is determined to be 0.208 cubic kilometers.

PREREQUISITES
  • Understanding of area conversion (hectares to square kilometers)
  • Basic knowledge of volume calculation (Volume = Area × Depth)
  • Familiarity with metric units (meters, kilometers)
  • Ability to perform unit conversions accurately
NEXT STEPS
  • Learn about unit conversions between hectares and square kilometers
  • Study volume calculation methods for irregular shapes
  • Explore the implications of open-pit mining on land use and environmental impact
  • Investigate mathematical modeling techniques for resource extraction calculations
USEFUL FOR

This discussion is beneficial for students studying environmental science, civil engineering, and mathematics, particularly those interested in land measurement and resource extraction calculations.

lgen0290
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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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