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Chapter 1: Problem 16

A unit of area, often used in expressing areas of land, is the hectare, defined as \(10^{4} \mathrm{~m}^{2}\). An open-pit coal mine consumes 77 hectares of land, down to a depth of \(26 \mathrm{~m}\), each year. What volume of earth, in cubic kilometers, is removed in this time?

Short Answer

Expert verified
The volume of earth removed each year is 0.02002 cubic kilometers

Step by step solution

01

Convert area from hectares to square meters

Given that 1 hectare equals \(10^{4} m^{2}\), the total area is \(77 hectares * 10^{4} m^{2}/hectare = 770000 m^{2}\)
02

Calculate volume in cubic meters

The volume in cubic meters can be calculated by multiplying the area by the depth. Volume = area * depth = \(770000 m^{2} * 26 m = 20020000 m^{3}\).
03

Convert volume from cubic meters to cubic kilometers

Since 1 cubic kilometer equals \(10^{9} m^{3}\), we divided the volume in cubic meters by \(10^{9} m^{3}/km^{3}\) to get the volume in cubic kilometers. Volume = \(20020000 m^{3}/10^{9} m^{3}/km^{3} = 0.02002 km^{3}\)

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