To find the total cost for 12 golden circle pendants, we can follow these steps:
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Calculate the volume of gold needed for one circle: Each circle is made of 10 cm³ of gold.
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Calculate the total volume of gold for 12 circles: \[ \text{Total volume for 12 circles} = 10 , \text{cm}^3 \times 12 = 120 , \text{cm}^3 \]
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Calculate the total mass of gold needed: The mass of gold can be calculated using the density of gold: \[ \text{Mass} = \text{Volume} \times \text{Density} \] We know the density of gold is 19.32 grams per cubic centimeter, so: \[ \text{Total mass} = 120 , \text{cm}^3 \times 19.32 , \text{g/cm}^3 = 2318.4 , \text{grams} \]
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Calculate the total cost of the gold: Given that gold costs $60 per gram, we can find the total cost: \[ \text{Total cost} = \text{Total mass} \times \text{Cost per gram} \] \[ \text{Total cost} = 2318.4 , \text{grams} \times 60 , \text{USD/g} = 139104 , \text{USD} \]
Thus, the total cost for 12 golden circles is $139,104.