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
21.08 g
21.08 g
1.84 g
1.84 g
22.10 g
22.10 g
Responses
2.202 g
2.202 g
21.08 g
21.08 g
1.84 g
1.84 g
22.10 g
22.10 g
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 the silver and then use that volume to find the mass of gold.
1. **Calculate the volume of silver:**
\[
\text{Volume of silver} = \frac{\text{mass of silver}}{\text{density of silver}} = \frac{12 \, \text{g}}{10.49 \, \text{g/cm}^3}
\]
\[
\text{Volume of silver} \approx 1.144 \, \text{cm}^3
\]
2. **Now, use this volume to find the mass of gold:**
\[
\text{Mass of gold} = \text{density of gold} \times \text{volume of silver} = 19.32 \, \text{g/cm}^3 \times 1.144 \, \text{cm}^3
\]
\[
\text{Mass of gold} \approx 22.10 \, \text{g}
\]
Therefore, the mass of gold that has the same volume as 12 grams of silver is approximately **22.10 grams**.
1. **Calculate the volume of silver:**
\[
\text{Volume of silver} = \frac{\text{mass of silver}}{\text{density of silver}} = \frac{12 \, \text{g}}{10.49 \, \text{g/cm}^3}
\]
\[
\text{Volume of silver} \approx 1.144 \, \text{cm}^3
\]
2. **Now, use this volume to find the mass of gold:**
\[
\text{Mass of gold} = \text{density of gold} \times \text{volume of silver} = 19.32 \, \text{g/cm}^3 \times 1.144 \, \text{cm}^3
\]
\[
\text{Mass of gold} \approx 22.10 \, \text{g}
\]
Therefore, the mass of gold that has the same volume as 12 grams of silver is approximately **22.10 grams**.