How many times will the earth be covered by 2,432,902,008,176,640,000 quarters or the same number of Swedish crowns?
A USA quarter is 2.4 cm in diameter, a Swedish crown is 2.5 cm in diameter.
The earth is 6371.315 miles in diameter. The surface of a sphere or globe is calculated
according to the formula: 4*pi*(radius)2 where pi is 3.141593. Therefore, the surface area of the
earth is 4*pi*(6371.315/2)2 = 127,528,738.6753106 square miles (or 127.5 million square miles).
A mile is 5280 feet, with 12 inches to a foot,
and one inch is 2.54 cm so there are 2.54*12 = 30.48 cm per foot and
30.48*5280 = 160,934.4 cm in a mile. Thus, a square mile is 160,934.4 cm * 160,934.4 cm = 25,899,882,109.2 cm2 or almost
26 billion square centimeters in a square mile. To find the number of square cm on the surface of the earth we multiply
25,899,882,109.2 cm2 by 127,528,738.6753106 miles2 which equals 3,302,979,425,499,030,000 square cm on the earth!
A quarter fits neatly in a square of the diameter of the quarter, or
2.4 cm, which is 2.4*2.4 = 5.76 cm2, and for a Swedish crown (2.5*2.5 = 6.25). Now we must divide the surface area of the
world by the surface area of a "square" quarter (or crown) to get the number of quarters needed to cover the earth. This is
3,302,979,425,499,030,000 / 5.76 = 573,433,905,251,809,900 quarters and
3,302,979,425,499,030,000 / 6.25 = 528,476,708,079,844,700 crowns.
Finally, we have to divide the fabulous number of
2,432,902,008,176,640,000 by the number of quarters covering the earth (573,433,905,251,809,900) to find out
how many earths the quarters would cover. The answer is 4.24 earths! The same number of Swedish crowns
would cover 4.6 earths since the crown is slightly larger than the quarter. If I had a puzzel with just one more
square (or 21 squares) then the number of earths covered would be 21 times greater (or 4.24*21 = 89 earths) - do you know why?
How many more earths would be covered if there were just two squares more than 20?