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 g
1.84 g

Answer 1

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.

The formula for volume based on density is:

\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]

Given that the density of silver is \(10.49 \, \text{g/cm}^3\) and the mass of silver is \(12 \, \text{g}\):

\[
\text{Volume of silver} = \frac{12 \, \text{g}}{10.49 \, \text{g/cm}^3} \approx 1.144 \, \text{cm}^3
\]

Now, we will use this volume to find the mass of gold that will occupy the same volume.

The density of gold is \(19.32 \, \text{g/cm}^3\).

Using the same formula for volume but rearranged to find mass:

\[
\text{Mass} = \text{Volume} \times \text{Density}
\]

Substituting the volume of silver into this formula for gold:

\[
\text{Mass of gold} = 1.144 \, \text{cm}^3 \times 19.32 \, \text{g/cm}^3 \approx 22.08 \, \text{g}
\]

Rounding to two decimal places, we get approximately \(22.10 \, \text{g}\).

Thus, the answer is:

**22.10 g**