If a gold coin was worth a billion dollars, how big would the coin be in diameter?
Jean Louis, Since 2009, trader, buyer, seller of scrap and recycled gold
According to the price of gold being today US $1197 for a troy ounce, a billion dollars would contain 835421 troy ounces (rounded). That is 25984525 grams or 25984 kilograms or 25.98 tonnes of gold. Considering that 19.3 tonnes of gold may fit into one cubic meter, the volume that 25.98 tonnes would occupy would be 1.34 cubic meters.
A coin is geometrical form of cylinder. We would need first to know the height of the coin (h) or its thickness. Such a large coin should have some thickness of 10 centimeters as example. The formula to calculate volume is V = PI x r2 x h. We know the volume is 1.34 cubic meters. h or height is 0.1 meter or 10 centimeter. We know PI and we just miss the radius. Thus volume divided by pi divided by h or height, would give the radius of the coin. Thus 1.34 meter divided by 0.10 meters divided by PI 3.1415926535897932385L0 (according to my Lisp programming language) give the radius of 4.26 meters. The is square radius (r2). The square root should be: 2.0639767440550294.
The radius is a straight line from the center of the circle to its perimeter, so the length of such coin would be double of the square root or 4.12 meters with its height or thickness being 10 centimeters.
When we wish to verify the formula, we would try to multiply PI with the radius multiplied by radius multiplied by height. So 3.1415926535897932385L0 multiplied by 2.0639767440550294 multiplied by 2.0639767440550294 multiplied by 0.1 meters thickness would gives us approximately again the 1.34 cubic meters of volume.
The diameter would be 4.26 meters provided that thickness of a coin is 10 centimeters.
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