A unit of area often used in measuring land areas is the hectare, defined as 104 m2. An open-pit coal mine consumes 72 hectares of land, down to a depth of 29 m, each year. What volume of earth, in cubic kilometers, is removed in this time?
The volume of earth removed is a rectangular prism, the volume of which is the planar area multiplied by the depth.
V = 72 hectares * 29 m
= 72*104 m² * 29 m
= 72*104*29 m³
Now one cubic kilometer contains
(1000)³ m³
= 1,000,000,000 m³
All you need to do is to convert the previous answer into km³.
.0207 km3
To find the volume of earth removed, we need to calculate the volume of the open-pit coal mine.
First, let's convert the area of the coal mine from hectares to square meters:
72 hectares * 10,000 square meters/hectare = 720,000 square meters
Next, we can calculate the volume by multiplying the area by the depth:
720,000 square meters * 29 meters = 20,880,000 cubic meters
However, the question asks for the volume of earth in cubic kilometers. To convert from cubic meters to cubic kilometers, we divide by 1,000,000,000 (since there are 1 billion cubic meters in a cubic kilometer):
20,880,000 cubic meters / 1,000,000,000 cubic meters/cubic kilometer = 0.02088 cubic kilometers
Therefore, approximately 0.02088 cubic kilometers of earth is removed each year from the open-pit coal mine.