A unit of area often used in measuring land areas is the hectare, defined as 104 m2. An open-pit coal mine consumes 99 hectares of land, down to a depth of 28 m, each year. What volume of earth, in cubic kilometers, is removed in this time?

To find the volume of earth removed, let's first convert the given measurements to the same unit.

1 hectare = 10,000 m² (since 1 hectare = 10,000 m²)

So, 99 hectares = 99 × 10,000 m² = 990,000 m².

Now, let's calculate the volume of earth removed. The formula for calculating the volume of a rectangular prism (which represents the section of land removed in this case) is length × width × height.

In this case, the length and width are equal to the given area of 990,000 m², and the height is the given depth of 28 m.

Volume = length × width × height = 990,000 m² × 990,000 m² × 28 m.

To convert the volume to cubic kilometers, we need to convert the units of meters to kilometers. Since 1 kilometer = 1000 meters, we can divide the volume by (1000 m)³ to get the volume in cubic kilometers.

Volume in cubic kilometers = (990,000 m² × 990,000 m² × 28 m) / (1000 m)³.

Now, let's calculate the volume.

Volume = (990,000 × 990,000 × 28) / (1000)³ = (990,000 × 990,000 × 28) / (1,000,000,000).

Evaluating this equation, we get:

Volume = 27.78336 cubic kilometers.

Therefore, approximately 27.78336 cubic kilometers of earth is removed each year.

volume: 99hectare*10^4 m^2/hectare*28m*(1km/10^3 m)3