Estimate the total number of bacteria and other prokaryotes in the biosphere of the earth. (assume the bacteria are found to a depth d = 1000 m below earth's surface, and that there are an average of 100 bacteria in every 1 mm3 of volume.)

Since the Earth is almost spherical in shape, we are actually to find first the volume of the spherical segment at a depth of 1,000 m. The radius of the Earth is 6,371,000 meters. The volume of a spherical segment is:

V = 1/3*πh² (3r - h)

Substituting the values and making sure the units is in mm,

V = 1/3*π (1000 m * 1000 mm/1 m) ²[3 (6,371,000 m * 1000 mm/1 m) - (1000 m * 1000 mm/1 m) ]

V = 2*10²² mm³

Thus, the total amount of bacteria is:

2*10²² mm³ * 100 bacteria/1 mm³ = 2*10²⁴ bacteria