Question
The density of silver is 10.49 g/cm3 , and the density of gold is 19.32 g/cm3 . What mass of gold will have the same volume as 12 grams of silver?(1 point) Responses 2.202 g 2.202 g 22.10 g 22.10 g 21.08 g 21.08 g 1.84 graphing calculator
Answers
GPT-4o mini
To find the mass of gold that has the same volume as 12 grams of silver, we first need to calculate the volume of silver and then use the density of gold to find the corresponding mass.
1. **Calculate the volume of silver**:
The formula for volume based on mass and density is:
\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]
For silver:
- Mass = 12 g
- Density = 10.49 g/cm³
\[
\text{Volume of silver} = \frac{12 \, \text{g}}{10.49 \, \text{g/cm}^3} \approx 1.144 \, \text{cm}^3
\]
2. **Use the volume of silver to find the mass of gold**:
Now, use the density of gold to find the mass that occupies the same volume:
For gold:
- Density = 19.32 g/cm³
Rearranging the volume formula for mass gives:
\[
\text{Mass} = \text{Density} \times \text{Volume}
\]
\[
\text{Mass of gold} = 19.32 \, \text{g/cm}^3 \times 1.144 \, \text{cm}^3 \approx 22.107 \, \text{g}
\]
So, the mass of gold that has the same volume as 12 grams of silver is approximately **22.10 g**.
1. **Calculate the volume of silver**:
The formula for volume based on mass and density is:
\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]
For silver:
- Mass = 12 g
- Density = 10.49 g/cm³
\[
\text{Volume of silver} = \frac{12 \, \text{g}}{10.49 \, \text{g/cm}^3} \approx 1.144 \, \text{cm}^3
\]
2. **Use the volume of silver to find the mass of gold**:
Now, use the density of gold to find the mass that occupies the same volume:
For gold:
- Density = 19.32 g/cm³
Rearranging the volume formula for mass gives:
\[
\text{Mass} = \text{Density} \times \text{Volume}
\]
\[
\text{Mass of gold} = 19.32 \, \text{g/cm}^3 \times 1.144 \, \text{cm}^3 \approx 22.107 \, \text{g}
\]
So, the mass of gold that has the same volume as 12 grams of silver is approximately **22.10 g**.