Mountain on a Ball

An official NBA basketball is 9.39 inches in diameter (as best I am able to determine from websites which do not all give the same info). If the earth were reduced to the side of a basketball, how big of a bump would Mount Everest make on the surface?

Answer:

About twice the thickness of a sheet of paper--probably indistinguishable from the normal texture of a basketball's surface.

Calculation: Mount Everest is 29,028 feet high. Since there are 5,280 feet in a mile, this is 29,028/5,280 = 5.5 miles high. The radius of the earth is 4000 miles. The radius of the basketball is 9.39/2 = 4.7 inches. Therefore, 4000 is to 7, as 4.5 is to the height of the bump. Therefore, the height of the bump = 7/4000 of 4.5 inches, which is .0079 inches, or less than one 100th of an inch.

A ream (500 sheets) of standard, 20-weight office copy paper is about 2 inches thick. Therefore, 1 inch contains the thickness of about 250 sheets of paper--so about 2 1/2 sheets of paper per one hundredth of an inch. Therefore, Mount Everest would be the height of about 2 thicknesses of a sheet of paper.