Question

In: Chemistry

The average density of planet earth is 5.52 g/cm3. Knowing that Earth has a mass of...

The average density of planet earth is 5.52 g/cm3. Knowing that Earth has a mass of 5.97*10^27g, determine the earth radius in miles. ( 1 mile = 1609 meters).

Solutions

Expert Solution

We have,
   density of the Earth = 5.52 g/cm3
and a mass of the Earth = 5.97x1027g

Therefore, volume of the Earth = mass/density = (5.97x1027g) / (5.52 g/cm3)
                                               = 1.08x1027 cm3
   We know that, volume of circle = (4/3)πr3 = 1.08x1027 cm3
                                           r3 = 0.258 1027cm3
                                           r = 0.637 x 109 cm
                                           r = 0.637 x 109 x 10-2 m
                                               = 0.637 x 107 meters
                                           r = 6.37 x 106 /1609 miles
                                          
                                           r = 3.96 x 103 miles
   Therefore, the radius of the Earth is = 3.96 x 103 miles = 3960 miles


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