Lecture Notes: Calculating Volume of Cuboids and Cubes

Volume of Cuboids

• Formula: Volume (V) = Length (L) × Width (W) × Height (H)
• Example:
  • Given:
    • Length = 8 cm
    • Width = 6 cm
    • Height = 5 cm
  • Volume calculation: 8 × 6 × 5 = 240 cubic centimeters (cm³)
• Units: Volume is always measured in cubic units (e.g., cm³) because it is a measure of three-dimensional space.

Volume of Cubes

• Definition: A cube is a special type of cuboid where all sides are equal.
• Formula: Volume (V) = Side Length (L) × Side Length (L) × Side Length (L) or L³
• Example:
  • Given: Edge Length = 5 cm
  • Volume calculation: 5 × 5 × 5 = 5³ = 125 cubic centimeters (cm³)

Exam Style Question

• Question: Given a cuboid with:
  • Width = 5 cm
  • Height = 7 cm
  • Total Volume = 350 cm³
• Objective: Find the cuboid's length.
• Steps:
  1. Use the formula for cuboid volume: V = L × W × H
  2. Rearrange to solve for Length (L):
     • L = Volume ÷ (Width × Height)
  3. Substitute the values:
     • L = 350 ÷ (5 × 7)
     • L = 350 ÷ 35 = 10 cm

Conclusion

• The cuboid's length is 10 cm.
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