Final answer:
To calculate the dollar value of a 78 kg gold nugget, convert the weight to grams, use the density to find the volume, and then multiply the volume by the price per cubic centimeter. The calculated value comes out to be $3,318,771.642.
Step-by-step explanation:
The student is asking about the calculation of the dollar value of a gold nugget based on its weight, the density of gold, and the price per cubic centimeter. To find the value of the nugget, first convert its weight from kilograms to grams since the density of gold is given in grams per cubic centimeter (g/cm³). One kilogram equals 1000 grams, so a 78 kg nugget would be equal to 78000 grams.
Next, we use the density of gold to determine the volume of the nugget. The formula for density is mass/volume, so the volume (V) can be calculated by dividing the mass (M) by the density (D), V = M/D. With the mass being 78000 grams and the density being 19.32 g/cm³, the volume is 78000/19.32 = 4037.461 cm³.
Finally, to find the dollar value of the gold nugget, multiply the volume by the price of gold per cubic centimeter. The price of gold is $822 per cm³, so the value (Value) of the gold nugget is volume (V) times price per cm³ (P): Value = V * P = 4037.461 cm³ * $822/cm³ = $3,318,771.642.