Lesson on Calculating Density

Introduction

• Density Formula: Density is calculated using the formula: [ \text{Density} = \frac{\text{Mass}}{\text{Volume}} ]
• Density is expressed in units of mass per volume, such as grams per cubic centimeter (g/cm³).

Example Problems

Question 1

• Problem: Calculate the density of a piece of metal with:
  • Mass = 12 grams
  • Volume = 6 cm³
• Solution:
  • Density = ( \frac{12}{6} = 2 ) g/cm³
• Result: Density of the metal is 2 g/cm³.

Question 2

• Problem: Calculate the density of a model with:
  • Mass = 40 grams
  • Volume = 120 cm³
• Solution:
  • Density = ( \frac{40}{120} = \frac{1}{3} ) or approximately 0.3 recurring
• Result: Density of the model is approximately 0.3 g/cm³.

Additional Practice

Cube Density Calculation

• Task: Calculate the density of a cube
  • Step 1: Calculate the volume of the cuboid
    • Area of the face = 6 cm × 4 cm = 24 cm²
    • Volume = Area × Depth = 24 cm² × 3 cm = 72 cm³
  • Step 2: Convert mass from kg to g
    • Mass = 0.15 kg = 150 grams
  • Step 3: Calculate density
    • Density = ( \frac{150}{72} \approx 2.1 ) g/cm³

Final Question

• Problem: Given a density of 2.25 g/cm³, find the mass of a cuboid with:
  • Volume calculated by cross-sectional area
    • Area = 10 cm × 12 cm = 120 cm²
    • Volume = 120 cm² × 3 cm = 360 cm³
• Solution:
  • Set up equation: 2.25 = ( \frac{\text{mass}}{360} )
  • Solve for mass by multiplying both sides by 360
  • Mass = 2.25 × 360 = 810 grams

Conclusion

• Thank you for watching.
• The lesson covered the calculation of density using mass and volume, and provided practice problems to reinforce the concept.