How many drops in all the oceans?

[Lemniscate]

Homework Statement

Simple question, but I don't know how to correctly approach it.

How many drops of water are in all the oceans on earth? Assume that 1cm^3 contains 25 drops of water.

Homework Equations

The average depth of the ocean is 4 km. I know I will have to convert to cm.
Radius of Earth: 6400 km
About 70% of the Earth is covered by oceans.

The Attempt at a Solution

Need help setting up the problem correctly.
I've tried various things. I'm not sure if I have to use the surface area of a sphere or the volume of a sphere.

I have to subtract the depth of the oceans (4km) from 6400km...?

 

[mgb_phys]

Find the surface area of the earth, then take the proportion of this that is covered by water.
Then imagine unrolling this areas as a flat map, not find the volume of a slab of water of this flat area and 4km high.

Then convert km^3 to cm^3

 

[Lemniscate]

mgb_phys,
by doing what you advised, I obtained a surface area of 5.15 x 10^8 km^2 times .70, which gave me a total of 3.6 x 10^8 km^2 roughly.

3.6 x 10^8 km^2 times 4 km for the depth gives me a volume of 1.44 x 10^14 cm ^3 (once I conver to cm).

Am I missing something? Because this is not the correct answer.

The question is asking me for the amount of drops of water. I should be multiplying my final answer, 1.44 x 10^14 cm ^3, by 25 (1cm^3 = 25 drops).

Where am I making a mistake?

 

[ideasrule]

1 km^3 = (1 00 000 cm)*(1 00 000 cm)*(1 00 000 cm)=10^15 cm^3, not 10^5 cm^3.

 

[Lemniscate]

Oops. I see what I did wrong.

Thanks to both of you!