To find the mass of the gold piece, we will use the formula:
\[ \text{mass} = \text{density} \times \text{volume} \]
According to the question, the density of gold is given as 19.3 grams per cubic centimeter (g/cm³), and we have a piece of gold with a volume of 45 cubic centimeters (cm³).
Now we can plug these values into the formula to calculate the mass:
\[ \text{mass} = 19.3 \, \text{g/cm³} \times 45 \, \text{cm³} \]
To perform the multiplication:
\[ \text{mass} = 868.5 \, \text{g} \]
So, the mass of a 45 cm³ piece of gold is 868.5 grams, which corresponds to option C.
