Determining the volume (\(V\)) of an object is crucial for various applications in science and industry. The volume can be calculated using the formula:
\[ V = \dfrac{m}{\rho} \]
Where:
- \(V\) is the volume of the object (in cubic meters, m³)
- \(m\) is the mass of the object (in kilograms, kg)
- \(\rho\) is the density of the object (in kilograms per cubic meter, kg/m³)
Example 1: Determining the Volume of a Gold Bar
Problem: A gold bar has a mass of 12 kg and a density of 19300 kg/m³. What is the volume of the gold bar?
Calculation:
Given:
- \(m = 12 \, \text{kg}\)
- \(\rho = 19300 \, \text{kg/m}^3\)
Using the formula:
\[ V = \dfrac{m}{\rho} = \dfrac{12}{19300} = 0.000621 \, \text{m}^3 \]
Answer: The volume of the gold bar is 0.000621 m³.
Example 2: Determining the Volume of a Lead Block
Problem: A lead block has a mass of 20 kg and a density of 11340 kg/m³. What is the volume of the lead block?
Calculation:
Given:
- \(m = 20 \, \text{kg}\)
- \(\rho = 11340 \, \text{kg/m}^3\)
Using the formula:
\[ V = \dfrac{m}{\rho} = \dfrac{20}{11340} = 0.00176 \, \text{m}^3 \]
Answer: The volume of the lead block is 0.00176 m³.
Example 3: Determining the Volume of a Glass Vase
Problem: A glass vase has a mass of 1.5 kg and a density of 2500 kg/m³. What is the volume of the glass vase?
Calculation:
Given:
- \(m = 1.5 \, \text{kg}\)
- \(\rho = 2500 \, \text{kg/m}^3\)
Using the formula:
\[ V = \dfrac{m}{\rho} = \dfrac{1.5}{2500} = 0.0006 \, \text{m}^3 \]
Answer: The volume of the glass vase is 0.0006 m³.
