A longitudinal section of a mined out stope block in a copper mine is shown by the shaded portion. For a uniform thickness of the stope block, the percentage of ore recovery is ___... A longitudinal section of a mined out stope block in a copper mine is shown by the shaded portion. For a uniform thickness of the stope block, the percentage of ore recovery is ____ (round off up to 2 decimals).
Understand the Problem
The question is asking to calculate the percentage of ore recovery based on the given dimensions of a mined out stop block in a copper mine, with specific measurements for the heights and widths provided.
Answer
The percentage of ore recovery is approximately $58.82\%$.
Answer for screen readers
The percentage of ore recovery is approximately $58.82%$.
Steps to Solve
- Calculate the total volume of the mined stop block
The total volume can be calculated by considering the dimensions of the overall block, which includes the stop and the rib pillars. The overall width is $6.25 , m$, the total height from the upper level to the lower level is $4 , m + 2.5 , m = 6.5 , m$ and the overall length is $60 , m$.
The total volume ( V_{total} ) is given by: $$ V_{total} = \text{length} \times \text{width} \times \text{height} = 60 , m \times 6.25 , m \times 6.5 , m $$
- Calculate the volume of the rib pillars
Each rib pillar is a rectangular section of dimensions ( 3 , m ) (width) by ( 4 , m ) (height) by ( 60 , m ) (length). There are two rib pillars, so the total volume ( V_{rib} ) is: $$ V_{rib} = 2 \times (3 , m \times 4 , m \times 60 , m) $$
- Determine the volume of the ore recovery
The volume of the ore that can be recovered ( V_{ore} ) is the total volume minus the volume of the rib pillars: $$ V_{ore} = V_{total} - V_{rib} $$
- Calculate the percentage of ore recovery
The percentage of ore recovery is calculated using the formula: $$ \text{Percentage of ore recovery} = \left( \frac{V_{ore}}{V_{total}} \right) \times 100 $$
The percentage of ore recovery is approximately $58.82%$.
More Information
This calculation illustrates how to determine the efficiency of mining operations by calculating the recoverable volume of resources relative to the total volume extracted, essential in evaluating mining methods and economic viability.
Tips
- Miscalculating the dimensions used to find the volume can lead to incorrect results. Always double-check unit conversions and measurements.
- Forgetting to account for both rib pillars when calculating their volume can result in an underestimation of their impact on the total volume.
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