Lecture Notes: Calculating Density, Mass, and Volume

Key Concepts

Formula Triangle (DMV Triangle)

• D: Density
• M: Mass
• V: Volume
• Mnemonic: "DMV" (Density, Mass, Volume)

Formulas

• Density ($D$): $D = \frac{M}{V}$
• Mass ($M$): $M = D \times V$
• Volume ($V$): $V = \frac{M}{D}$

Examples

Example 1: Calculating Density

• Problem: A cake has a mass of 500 grams and a volume of 2500 cm³. What is the density?
• Solution:
  • Formula: $D = \frac{M}{V}$
  • Given: $M = 500$ grams, $V = 2500$ cm³
  • Calculation: $D = \frac{500}{2500} = 0.2$ grams/cm³

Example 2: Calculating Density

• Problem: A block of wood has a mass of 6 grams and a volume of 12 cm³. What is the density?
• Solution:
  • Formula: $D = \frac{M}{V}$
  • Given: $M = 6$ grams, $V = 12$ cm³
  • Calculation: $D = \frac{6}{12} = 0.5$ grams/cm³

Example 3: Calculating Mass

• Problem: The density of a substance is 8 grams/cm³, and the volume is 25 cm³. What is the mass?
• Solution:
  • Formula: $M = D \times V$
  • Given: $D = 8$ grams/cm³, $V = 25$ cm³
  • Calculation: $M = 8 \times 25 = 200$ grams
  • Unit check:
    • $\frac{grams}{cm³} \times cm³ = grams$

Example 4: Calculating Volume

• Problem: A weight has a mass of 820 grams and a density of 5 grams/cm³. What is the volume?
• Solution:
  • Formula: $V = \frac{M}{D}$
  • Given: $M = 820$ grams, $D = 5$ grams/cm³
  • Calculation: $V = \frac{820}{5} = 164$ cm³
  • Unit check:
    • $\frac{grams}{\frac{grams}{cm³}} = cm³$

Conclusion

• Remember the DMV Triangle (Density, Mass, Volume) for calculations
• Use appropriate formulas based on the required variable (D, M, or V)
• Always check units to ensure they cancel out correctly

Reminders

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