Calculating approx. Values in km3, m3, cubic miles, and gallons

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SUMMARY

The discussion focuses on calculating the approximate volume of Earth's oceans using its radius of 6370 km and an average depth of 12,000 feet. Participants emphasize the importance of calculating the surface area of the Earth as a sphere using the formula 4 * Pi * R², then multiplying by 70% to account for water coverage. The final volume is derived by multiplying the water-covered area by the average depth, with necessary unit conversions to obtain results in km³, m³, cubic miles, and gallons. This method simplifies the calculation process compared to more complex integration approaches.

PREREQUISITES
  • Understanding of basic geometry, specifically the formula for the surface area of a sphere.
  • Knowledge of unit conversions between kilometers, cubic meters, cubic miles, and gallons.
  • Familiarity with the concept of percentage to calculate water coverage.
  • Basic mathematical skills for multiplication and area calculations.
NEXT STEPS
  • Learn about the mathematical derivation of the surface area of a sphere.
  • Research unit conversion techniques for volume measurements.
  • Explore the implications of Earth's water coverage on global climate and ecosystems.
  • Investigate advanced integration techniques for volume calculations in irregular shapes.
USEFUL FOR

Students in mathematics or environmental science, educators teaching volume calculations, and anyone interested in understanding Earth's water distribution and its implications.

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Homework Statement


Earth’s radius is 6370 km and approximately 70% of
its surface is covered with water, to an average depth
of 12,000 feet. Calculate the approximate volume, in
km
3
, m
3
, cubic miles and gallons of Earth’s oceans.


Homework Equations





The Attempt at a Solution




I was told to find the area and to multiply by the avrg depth but i am still confused.
 
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Welcome to PF.
You can calculate the total volume of the Earth and then subtract the non water portions.
1. Calculate total volume in desired unit.
2. Calculate volume of "inner" portion.
3. Subtract inner portion from total volume then multiply by 0.7 to account for 70% water coverage.
 
Isn't it a lot easier than that?

Just calculate the surface area of the sphere (4 * Pi * R2).
Multiply by 70/100 to get the area covered by water.
Multiply by the average depth.

Obviously convert everything to appropriate units first. For example if you convert the average depth to km the answer will be in km3.

Then convert to the other units required.
 
Yes your method is easier. I just couldn't get away from integration in my head so I pieced it out for the OP in not quite as eloquent manner as you did...
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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