The radius (r) of the earth at the equator is about 6380 (6.38 times 10^3) km. a

Question

The radius (r) of the earth at the equator is about 6380 (6.38 times 10^3) km. a. Calculate Earth's circumference (remember, circumference of a sphere = 2 pi r)? How does this value compare with that found by Eratosthenes in the third century BC? b. what is Earth's volume (remember, volume of a sphere = 4/3 pi r^3)? c. What is the volume of the oceans assuming an average depth of 3750 m and an area of about 3.62 times 10^8 km^2? d. What is the fraction of ocean volume to Earth's total volume? Use scientific notation, show your work and express your final answers using the proper number of significant figures!

Explanation / Answer

a. By calculation Circumference of earth = 2 X pi X radius

= 2 X 3.14 X 6380 km

= 40,066.4 km

Eratosthenes calculated the circumference of earth as nearly 25000 miles. i.e., 40,233.6 km, which is roughly 167.2 kms off original value.

b. Volume of earth = 4/3 X pi X r3

= 4/3 X 3.14 X 63803

= 1.087 X 1012 km3

c. Volume of ocean = Surface area X Depth

= 3.62 X 108 X 3.750

= 1.3575 X 10 9 km3

d) Fraction of Ocean volume to Earth's total volume = Ocean volume / Total volume of earth

=1.3575 X 109 / 1.087 X 1012

= 0.001248

Hope this helps

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