I wanted to calculate the height of water above a perfectly smooth earth sphere if all the water on earth surrounded the sphere.
I found the volume of all water on line to be 322.5 cu miles. Using a 400mile radius for my earth sphere, I calculated the volume of this sphere (268.082E9 cu miles) and then added the 322.5E6 cu miles of water and solved for the difference in the two radii (with and without surrounding water). Answer 1.6 miles.
All great, but then a friend did the calculation by dividing the surface area of my earth sphere (201.062E6 sq miles into the volume of water (322.5E6 cu miles) and got the same answer--1.6 mile high. He claims you can use the rectangular volume calculation and get the same answer as with the spherical volume calculation because somehow the earth's gravitational system equates the two.
I don't get it and think he is blowing smoke, but I can't figure out why I get the same answer using both methods (spherical and rectangular). Any help?