To calculate the density ([tex]\( \rho \)[/tex]) of a material, we use the formula:
[tex]\[
\rho = \frac{\text{mass}}{\text{volume}}
\][/tex]
Given:
- Volume ([tex]\( V \)[/tex]) = [tex]\( 25 \, \text{cm}^3 \)[/tex]
- Mass ([tex]\( m \)[/tex]) = [tex]\( 459 \, \text{g} \)[/tex]
First, we need to convert the mass from grams to kilograms, since the density is to be found in [tex]\( \text{kg/m}^3 \)[/tex].
1 gram (g) = 0.001 kilograms (kg)
Thus, the mass in kilograms is:
[tex]\[
m = 459 \, \text{g} \times 0.001 \, \frac{\text{kg}}{\text{g}} = 0.459 \, \text{kg}
\][/tex]
Next, we convert the volume from cubic centimeters ([tex]\( \text{cm}^3 \)[/tex]) to cubic meters ([tex]\( \text{m}^3 \)[/tex]), since we need the density in [tex]\( \text{kg/m}^3 \)[/tex].
1 cubic meter ([tex]\( \text{m}^3 \)[/tex]) = 1,000,000 cubic centimeters ([tex]\( \text{cm}^3 \)[/tex])
Thus, the volume in cubic meters is:
[tex]\[
V = 25 \, \text{cm}^3 \times \frac{1 \, \text{m}^3}{1,000,000 \, \text{cm}^3} = 25 \times 10^{-6} \, \text{m}^3 = 2.5 \times 10^{-5} \, \text{m}^3
\][/tex]
Now, we use the density formula:
[tex]\[
\rho = \frac{m}{V} = \frac{0.459 \, \text{kg}}{2.5 \times 10^{-5} \, \text{m}^3}
\][/tex]
Performing the division:
[tex]\[
\rho = \frac{0.459}{2.5 \times 10^{-5}} = 18360 \, \text{kg/m}^3
\][/tex]
Therefore, the density of the material is [tex]\( 18,360 \, \text{kg/m}^3 \)[/tex].
