Sure, let's go through the problem step by step to find the density of the material given the volume and mass.
1. Given:
- Volume ([tex]\( V \)[/tex]) = [tex]\( 25 \, \text{cm}^3 \)[/tex]
- Mass ([tex]\( m \)[/tex]) = [tex]\( 45 \, \text{grams} \)[/tex]
2. Convert the volume to cubic meters (m[tex]\(^3\)[/tex]):
- We know that [tex]\( 1 \, \text{cm}^3 \)[/tex] is equal to [tex]\( 1 \times 10^{-6} \, \text{m}^3 \)[/tex].
- Therefore, [tex]\( 25 \, \text{cm}^3 \)[/tex] is:
[tex]\[
25 \, \text{cm}^3 = 25 \times 10^{-6} \, \text{m}^3 = 2.5 \times 10^{-5} \, \text{m}^3
\][/tex]
3. Convert the mass to kilograms (kg):
- We know that [tex]\( 1 \, \text{gram} \)[/tex] is equal to [tex]\( 1 \times 10^{-3} \, \text{kg} \)[/tex].
- Therefore, [tex]\( 45 \, \text{grams} \)[/tex] is:
[tex]\[
45 \, \text{grams} = 45 \times 10^{-3} \, \text{kg} = 0.045 \, \text{kg}
\][/tex]
4. Calculate the density in [tex]\( \text{kg/m}^3 \)[/tex]:
- Density ([tex]\( \rho \)[/tex]) is defined as mass per unit volume.
- Using the formula [tex]\(\rho = \frac{m}{V}\)[/tex]:
[tex]\[
\rho = \frac{0.045 \, \text{kg}}{2.5 \times 10^{-5} \, \text{m}^3} = 1800 \, \text{kg/m}^3
\][/tex]
So, the density of the material is [tex]\( 1800 \, \text{kg/m}^3 \)[/tex].
