Noah, the Flood and Calculus

I saw the trailer of the movie Noah. It inspired me to ask my students in my calculus class a question as a bonus assignment.

If it rained for forty days and forty nights, the water filled up to the peak of Mount Ararat, how much water fell on earth by using the disk method of calculating volume of revolution in calculus.

Some of the equations may not display correctly on the browser.

Here are the assumptions and numbers:

The earth is an ellipsoid with an equatorial radius of a=6378.1 km and polar radius of b=6356.8 km.

Mount Ararat has a height of 5.137 km.

Here is the solution:

Equation of an ellipse: x^2/a^2 +y^2/b^2 =1 or y=b/a √(a^2-x^2 )


dV=πy^2 dx, ∴V=2π∫_0^a▒b^2/a^2 (a^2-x^2 )dx

I will not type in all the detail of the calculation,

for a_2= the radius of the earth plus the height of Mount Ararat,

and a_1 = the radius of the earth,

volume of water should be approximately 2.623×10^9 km3 or 2.623×10^18 m3

The mass of the water should be approximately 2.623×10^21 kg.

For forty days and forty nights, it is a total of 960 hours, the rate of rain fall is 535.1 cm/hour or 8.9 cm/min.

Volume of water coming down from heaven is 2.732×10^15 m3/hour.

Noah does not need an ark. He needs a submarine!


4 responses to “Noah, the Flood and Calculus

  • ljdemps56

    They also say that the water came from springs below.

    • Lee

      Hi ljdemps56,

      You beat me to it! (See Genesis 7:11; 8:2.) In Biblical geology, there is water both below and above the earth. The flood would come from both directions. And the earth was probably thought of as a flat square or disc about 1,500 miles across, perhaps floating on and surrounded by water. Just open the floodgates or pop the corks that keep out the water, and it could get inundated quite easily.

      Still a fun calculation. Even with a smaller, flat earth, that would be a lot of water! Makes no scientific sense to us today, but it would not have seemed outlandish for the original tellers and hearers of the story thousands of years ago.

      Not that they were concerned about the science involved. This narrative comes from a pre-scientific age. It wasn’t about how the world was created geologically or about the history of human civilization as we conceive of it today. It was really a story about our relationship with God and with one another, told in an ancient mythical, poetic, and symbolic language.

  • dragonfinger

    HAHA! I was preparing my calculus lessons. I tried to make my calculus class a bit more interesting. BTW, I’m NOT teaching in a Christian school. Otherwise, any fundamentalist would call this sacrilegious. I don’t even know any of my students are Christians, Muslims or atheists. Since the movie is a big box office hit, I think it is fun to mix comtemporary Hollywood culture, Bible, and calculus.

  • Pam Zee

    The movie does not reflect the true account of the Bible. No one really knows what the earth was before and after the flood. We just make a whole lot of assumptions and come to an answer we think it matches what we think it should be. No one has accounted for seismic activities that took place during and after the flood. The general image of the arc is not what it should be. It is not a boat and God closed the door on it. It never rained on earth before the flood.

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