# geometry

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In a game show, the prize is the amount of revolutions a coin would make in one kilometer times the value of the coin. Your choices are the dime or the quarter. A dime has a diameter of 188 millimeters and a quarter has a diameter of 25 millimeters. Which coin would you choose to roll for one kilometer? How much more money would you make by choosing that coin?

• geometry -

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• geometry -

My Canadian dime, same size as an American dime, is 18.8 mm
yours is like a small dinner plate

So one roll of the dime would cover π(18.8) mm
= 1.88π cm
1 km
= 100000 cm
so the number of rotations = 100000/(1.88π) = 16931
with a value of \$\$1693

for the quarter ...
one rotation covers 25π mm or 2.5 cm
number of rolls for a quarter in 1 km
= 100000/(2.5π) = 12732
with a value of .25(12732) = \$3183

the choice is obvious

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