A unit of area, often used in measuring land areas, is the hectare defined as `10^4 m^2` An open-pit coal mine consumes 75 hectares of land, down to a depth of 26 m, each year. What volume of earth, in a cubic kilometre, is removed in this time?

Options

A. 0.01
B. 0.02
C. 0.03
D. 0.04

Answer

To solve the problem, we need to calculate the volume of earth removed by the open-pit coal mine in cubic kilometers. Here’s a step-by-step breakdown of the solution:

### Step 1: Convert Hectares to Square Meters
We know that 1 hectare is defined as \(10^4 \, \text{m}^2\). Therefore, to find the area in square meters for 75 hectares, we multiply:

\[ \text{Area} = 75 \, \text{hectares} \times 10^4 \, \text{m}^2/\text{hectare} = 75 \times 10^4 \, \text{m}^2 = 750000 \, \text{m}^2 \]

### Step 2: Calculate the Volume in Cubic Meters
The volume \(V\) of earth removed can be calculated using the formula:

\[ V = \text{Area} \times \text{Depth} \]

Given that the depth is 26 m, we can substitute the values:

\[ V = 750000 \, \text{m}^2 \times 26 \, \text{m} = 19500000 \, \text{m}^3 \]

### Step 3: Convert Cubic Meters to Cubic Kilometers
To convert cubic meters to cubic kilometers, we use the conversion factor \(1 \, \text{km}^3 = 10^9 \, \text{m}^3\):

\[ V = \frac{19500000 \, \text{m}^3}{10^9 \, \text{m}^3/\text{km}^3} = \frac{19500000}{1000000000} \, \text{km}^3 = 0.0195 \, \text{km}^3 \]

### Step 4: Round the Result
Rounding \(0.0195 \, \text{km}^3\) to two decimal places gives us approximately:

\[ V \approx 0.02 \, \text{km}^3 \]

### Final Answer
The volume of earth removed each year by the coal mine is approximately \(0.02 \, \text{km}^3\).

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