Physics

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 $$75$$ hectare of land, down to a depth of $$26\ m$$, each year. What volume of earth, in cubic kilometers, is removed in this time?


SOLUTION
1 hectare =$$ 10^4 m^2$$

Area of pit, A = 75 hectare

convert hectare into m^2

A = $$75 \times10^4 m^2$$

depth, d = 26 m

Volume of earth removed is V.

V = area of pit x depth

V = A x d

V = $$75 \times 10^4 \times  26 = 1950 \times  10^4 m^3$$

Convert cubic metre into cubic km

$$1 m = 10^-3 km$$

$$1 m^3 = 10^-9 km^3$$

So,

V = 1950 \times 10^{4} \times 10^{-9}=0.0195km^{3}
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