Math Help

October 28th, 2008

$math help$
Question: I need help with a math problem. How many drops of water are in all the oceans in the world?

Assuming:

1cm^3 of water = 25 drops
Average depth of the oceans is 4km
Radius of the world is 6400 km
70% of the world is covered by the ocean

surface area of a sphere is S=4(pi)r^2

I need the answer in drops. Please explain how it was done.
Thank You VERY much.
answer must be expressed in one sig figure.

Answer: First you need to calculate the surface area of the earth using the formula for surface area of a sphere:

S=4(pi)r^2
S=4(pi)(6400)^2
S=514718105 km^2

but only 70% of the earth’s surface is water, so multiply by 0.7:

514718105 x 0.7 = 360302674 km^2

So now we have the surface area of the oceans, which average 4 km deep. Therefore very square km of surface area is 4 cubic km of water, so:

360302674 x 4 = 1441210696 cubic km of ocean water.

There are 1 million cc in one cubic meter, and another million cubic meters in one cubic kilometer. So that means we have 1,441,210,696 x 1,000,000 x 1,000,000 = 1.44 x 10^21 cc in the oceans

Using your statement that there are 25 drops in a cc, that means:

1.44 x 10^21 cc x 25 drops = 3.6 x 10^22 drops

There are 3.603 x 10^22 drops of water in the oceans.

Now let’s check that against some real world numbers:

The total volume in the Earth’s ocean has been calculated to be 1.3 billion cubic kilometers (1,300,000,000 km^3). So that means we have 1,300,000,000 x 1,000,000 x 1,000,000 = 1.3 x 10^21 cc in the oceans

Using your assumption that there are 25 drops in a cc, that means there are 3.25 x 10^22 drops of water in the oceans.

EDIT – You’ve added the requirement for 1 sig fig, so the answers are …

Your data: 4 x 10^22 drops or 40000000000000000000000 drops

Real world data: 3 x 10^22 drops or 30000000000000000000000 drops.

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