Imagine and calculate
Imagine that the earth shrunk and the oceans dried off. Would the earth be:
A) Smoother than a baseball but not a golf ball
B) Smoother than a golf ball but not a billiard ball
C) Smoother than a billiard ball
D) Rougher than all of the above
Does your intuition and calculations say the same thing?
Problem source: Martin Gardner via the Wordplay blog at New York Times.
June 14th, 2010 at 11:09 am
This one surprised me. My initial hypothesis was that the answer would end up being (B).
When I looked up the data for the average diameter of the Earth, the height of Mt. Everest, and the depth of the Mariana Trench, I realized that it was more likely to end up being (C).
Average Diameter of Earth: 12,756,320 meters
Height of Everest: 8,850 m
Depth of Mariana Trench: -11,033 m
If you allow the Earth to be considered spherical for the sake of easier calculations, then Earth’s deviation between its highest and lowest point is 0.15587%.
US Billiard balls are between 2.258 and 2.245 inches. [note: the page I found this data on unfortunately stated something about the smoothness of the earth. However, by the time I found this I already had my answer and it was unintentional so it doesn’t count as cheating.)
Billiard balls have a deviation between their highest and lowest points of 0.57739%.
Thus Earth is not only as smooth as a billiards ball but rather is an astounding 3.7x smoother!
Very strange fact.
June 14th, 2010 at 11:14 am
I’m 190.5 cm tall. If I were on the Earth when it were shrunk, my height would become 8.51 nanometers.