At the time this problem was written, the price of gold was $427 per ounce, while that of platinum was $866 an ounce. The "ounce" in this case is the troy ounce, which is equal to 31.1035 g. The density of gold is 19.3 g/cm^3 and that of platinum is 21.4 g/cm^3. a)If you find a spherical gold nugget worth 1.00 million dollars, what would be its diameter?

Question

At the time this problem was written, the price of gold was $427 per ounce, while that of platinum was $866 an ounce. The "ounce" in this case is the troy ounce, which is equal to 31.1035 g. The density of gold is 19.3 g/cm^3 and that of platinum is 21.4 g/cm^3. a)If you find a spherical gold nugget worth 1.00 million dollars, what would be its diameter?

b)How much would a platinum nugget of this size be worth?

Answer 1

$1,000,000 x(1 oz/$427) = ?? oz.

??oz x (31.1035 g/1 oz) = xx grams.
volume = xx grams/density = zz cm³.
Volume of a sphere = (4/3)*pi*r³. Solve for r and multiply by 2 since 2r = diameter.
b) is done the same way.

Answer 2

To solve this problem, we will need to calculate the volume of the gold nugget and then use that volume to determine its diameter. We will then use the density of platinum to calculate the weight of a platinum nugget with the same volume.

Let's start with part (a) and find the diameter of the gold nugget worth 1.00 million dollars.

To do this, we need to determine the volume of the gold nugget. Since we know the density of gold and the price per ounce, we can figure out the mass of the gold nugget using the formula:

mass = value / price

mass = 1,000,000 dollars / 427 dollars/ounce

To convert the mass from ounces to grams, we can use the conversion factor that states 1 troy ounce is equal to 31.1035 grams:

mass = (1,000,000 dollars / 427 dollars/ounce) * (1 troy ounce / 31.1035 grams)

Now, we can calculate the volume of the gold nugget using the density of gold:

volume = mass / density

volume = (mass / density) / (grams / cm^3)

Now, let's calculate the diameter of the gold nugget using the volume of a sphere formula:

volume = (4/3) * π * (diameter/2)^3

Simplifying this equation, we get:

diameter = (6 * volume / π)^(1/3)

Substituting the value of the volume we calculated earlier, we have:

diameter = (6 * [(mass / density) / (grams / cm^3)] / π)^(1/3)

Now we can plug in the known values and calculate the diameter.

For part (b), we will use the calculated volume of the gold nugget to find the weight of a platinum nugget with the same volume. We'll use the density of platinum to determine the mass of the platinum nugget and then calculate its value.

mass of platinum = volume * density of platinum

value of platinum = mass of platinum * price of platinum per gram

By following these steps, you can find the diameter of the gold nugget and the value of an equivalent platinum nugget.