Question

The density of silver is 10.49 g/cm3
10.49

g
/
cm
3
. If a sample of silver has a volume of 0.2 m3
0.2

m
3
, what is the mass of the sample?

Answer 1

To calculate the mass of the silver sample, we can use the formula:

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

First, we need to ensure that the units of density and volume are compatible. The density of silver is given as \(10.49 \, \text{g/cm}^3\), and the volume of the sample is given as \(0.2 \, \text{m}^3\).

1. **Convert the volume from cubic meters to cubic centimeters**:

Since \(1 \, \text{m}^3 = 1,000,000 \, \text{cm}^3\) (or \(1 \, \text{m}^3 = 10^6 \, \text{cm}^3\)), we convert:

\[
0.2 \, \text{m}^3 = 0.2 \times 1,000,000 \, \text{cm}^3 = 200,000 \, \text{cm}^3
\]

2. **Calculate the mass using the density**:

Now, we can use the density to find the mass:

\[
\text{Mass} = 10.49 \, \text{g/cm}^3 \times 200,000 \, \text{cm}^3
\]

Calculating this gives:

\[
\text{Mass} = 10.49 \times 200,000 = 2,098,000 \, \text{g}
\]

3. **Convert the mass to kilograms** (since \(1 \, \text{kg} = 1000 \, \text{g}\)):

\[
\text{Mass} = \frac{2,098,000 \, \text{g}}{1000} = 2098 \, \text{kg}
\]

Thus, the mass of the silver sample is **2098 kg**.