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

[kelpmonster1]

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.

 

[Bhumble]

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.

 

[CWatters]

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.

 

[Bhumble]

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...

 

[Nickie]

I would approach this problem by first converting all the units to a common unit, such as meters. The radius of the Earth in meters is 6,370,000 m. The average depth of the oceans in meters would be 12,000 feet converted to meters, which is approximately 3,658 m.

To calculate the volume of the oceans in cubic meters, we can use the formula for the volume of a sphere, V = (4/3)πr^3, where r is the radius. Plugging in the values, we get V = (4/3)π(6,370,000)^3 = 1.08 x 10^21 m^3.

To convert this to cubic kilometers, we can divide by 1 billion (since 1 km^3 = 1 billion m^3), giving us a volume of approximately 1.08 billion km^3.

To convert to cubic miles, we can use the conversion factor 1 km^3 = 0.239912 cubic miles, giving us a volume of approximately 258 million cubic miles.

Finally, to convert to gallons, we can use the conversion factor 1 cubic mile = 1.101 x 10^12 gallons, giving us a volume of approximately 284 billion gallons.

Therefore, the approximate volume of Earth's oceans in km^3 is 1.08 billion km^3, in m^3 is 1.08 x 10^21 m^3, in cubic miles is 258 million cubic miles, and in gallons is 284 billion gallons.