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?
?HUH???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????.......................................
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
To determine which coin is more suitable for rolling 1 kilometer, we need to calculate the number of revolutions each coin would make in that distance. Let's start with the dime:
The formula to calculate the number of revolutions a coin would make in a distance is:
Number of Revolutions = Distance / Circumference
The circumference of a circle is calculated by multiplying its diameter by π (pi). So, let's calculate the circumference of the dime:
Circumference of Dime = Diameter of Dime * π
Circumference of Dime = 188 mm * π
Next, to find the number of revolutions, we'll divide the distance of 1 kilometer by the circumference in millimeters:
Number of Revolutions for Dime = 1 km / Circumference of Dime
Repeat the same calculations for the quarter:
Circumference of Quarter = Diameter of Quarter * π
Circumference of Quarter = 25 mm * π
Number of Revolutions for Quarter = 1 km / Circumference of Quarter
Now that we have the number of revolutions for each coin, we can determine which coin would yield a higher prize:
Prize for Dime = Number of Revolutions for Dime * Value of Dime
Prize for Quarter = Number of Revolutions for Quarter * Value of Quarter
Compare the two prizes to determine which coin would yield more money:
Amount More = Prize for Quarter - Prize for Dime
By performing these calculations, you will be able to determine which coin would provide a higher prize and calculate the additional amount you would make by choosing that coin.