Question

A jewelry company makes golden circle pendants. Each circle is made of 10 cm3 of gold, and there are 19.32 grams of gold per cubic centimeter. If gold costs $60 per gram, what is the total cost for 12 golden circles?

Answer 1

To find the total cost for 12 golden circle pendants, we can follow these steps:

1. **Calculate the volume of gold needed for one circle**:
Each circle is made of 10 cm³ of gold.

2. **Calculate the total volume of gold for 12 circles**:
\[
\text{Total volume for 12 circles} = 10 \, \text{cm}^3 \times 12 = 120 \, \text{cm}^3
\]

3. **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:
\[
\text{Total mass} = 120 \, \text{cm}^3 \times 19.32 \, \text{g/cm}^3 = 2318.4 \, \text{grams}
\]

4. **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**.