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!