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 find the volume of earth removed by the open-pit coal mine in cubic kilometers, we can follow these steps:

### Step 1: Convert hectares to square meters
1 hectare is defined as \(10^4 \, \text{m}^2\). Therefore, for 75 hectares:
\[ \text{Area} = 75 \, \text{hectares} \times 10^4 \, \text{m}^2/\text{hectare} = 75 \times 10^4 \, \text{m}^2 \]

### Step 2: Calculate the volume in cubic meters
The volume \(V\) can be calculated using the formula:
\[ V = \text{Area} \times \text{Depth} \]
Given that the depth is 26 m:
\[ V = (75 \times 10^4 \, \text{m}^2) \times (26 \, \text{m}) = 1950 \times 10^4 \, \text{m}^3 \]

### Step 3: Convert cubic meters to cubic kilometers
To convert cubic meters to cubic kilometers, we use the conversion factor:
\[ 1 \, \text{km}^3 = 10^9 \, \text{m}^3 \]
Thus, to convert \(1950 \times 10^4 \, \text{m}^3\) to cubic kilometers:
\[ V = \frac{1950 \times 10^4 \, \text{m}^3}{10^9 \, \text{m}^3/\text{km}^3} = \frac{1950 \times 10^4}{10^9} \, \text{km}^3 = 1950 \times 10^{-5} \, \text{km}^3 = 0.195 \, \text{km}^3 \]

### Final Answer
The volume of earth removed each year is approximately:
\[ 0.195 \, \text{km}^3 \]