Answer :
Sure, let's solve this step-by-step:
### Problem Statement:
We need to find the density of a body that weighs 1200 kg and has a volume of 250,000 cm³. The final numerical answer should match the solution provided.
### Solution:
1. Convert the Volume from cm³ to m³:
The volume of the body is given as 250,000 cm³. To work with weight in kilograms (kg) and volume in cubic meters (m³), we first need to convert the volume from cubic centimeters to cubic meters.
The conversion factor is:
[tex]\[
1 \, \text{m³} = 1,000,000 \, \text{cm³}
\][/tex]
Therefore:
[tex]\[
\text{Volume in m³} = \frac{250,000 \, \text{cm³}}{1,000,000} = 0.25 \, \text{m³}
\][/tex]
2. Calculate the Density:
Density ([tex]\( \rho \)[/tex]) is defined as mass (weight) per unit volume. The formula for density is:
[tex]\[
\rho = \frac{\text{mass}}{\text{volume}}
\][/tex]
Given:
- Mass (weight) = 1200 kg
- Volume = 0.25 m³
Substituting these values into the density formula:
[tex]\[
\rho = \frac{1200 \, \text{kg}}{0.25 \, \text{m³}} = 4800 \, \text{kg/m³}
\][/tex]
Therefore, the density of the body is [tex]\(4800 \, \text{kg/m}³\)[/tex].
### Problem Statement:
We need to find the density of a body that weighs 1200 kg and has a volume of 250,000 cm³. The final numerical answer should match the solution provided.
### Solution:
1. Convert the Volume from cm³ to m³:
The volume of the body is given as 250,000 cm³. To work with weight in kilograms (kg) and volume in cubic meters (m³), we first need to convert the volume from cubic centimeters to cubic meters.
The conversion factor is:
[tex]\[
1 \, \text{m³} = 1,000,000 \, \text{cm³}
\][/tex]
Therefore:
[tex]\[
\text{Volume in m³} = \frac{250,000 \, \text{cm³}}{1,000,000} = 0.25 \, \text{m³}
\][/tex]
2. Calculate the Density:
Density ([tex]\( \rho \)[/tex]) is defined as mass (weight) per unit volume. The formula for density is:
[tex]\[
\rho = \frac{\text{mass}}{\text{volume}}
\][/tex]
Given:
- Mass (weight) = 1200 kg
- Volume = 0.25 m³
Substituting these values into the density formula:
[tex]\[
\rho = \frac{1200 \, \text{kg}}{0.25 \, \text{m³}} = 4800 \, \text{kg/m³}
\][/tex]
Therefore, the density of the body is [tex]\(4800 \, \text{kg/m}³\)[/tex].
