Show how you got the answer for parts a,b,c, and d. The answers are posted below.

1) One hectare, a unit of measure often used in measuring land areas, is defined to be 10^4 m^2. In an effort to dig to China, a desperate grad student digs a pit 15 m deep over an area of 3 hectares before he happily dies of exhaustion. What volume of earth has been exhumed? Express your answer in:

a) cubic meters

b) cubic kilometers.

Years later, a bionic but equally desperate grad student digs a pit of the same area and manages to tunnel directly through the center of the Earth to China. The Earth is approximately a sphere with a radius of 6,371 km. To nearest order of magnitude, estimate the volume of earth exhumed in:

c) cubic kilometers

d) as a fraction of the Earth's total volume.

Answers:

a) 4.5×10^5 m^3

b) 4.5?10^-4 km^3

c) 10^2 km^3

d) 10^-10