How to Calculate the Volume of a Trapezoidal Structure
Step 1: Volume of the Rectangular Base
The rectangular base is a prism. Its volume is calculated as:
Vrect = Length × Width × Depth
Input Data:
- Length (L) = 6 meters
- Width (b) = 5.6 meters
- Depth (d) = 0.450 meters
Calculation:
Vrect = 6 × 5.6 × 0.450
Vrect = 15.12 m³
The volume of the rectangular base is 15.12 cubic meters.
Step 2: Volume of the Trapezoidal Frustum
The trapezoidal frustum is a truncated pyramid. Its volume is calculated as:
Vfrustum = (h / 3) × (A1 + A2 + √(A1 × A2))
Step 2.1: Calculate Area of the Bottom Base (A1)
Input Data:
- Length (L1) = 6 meters
- Width (b1) = 5.6 meters
Calculation:
A1 = 6 × 5.6 = 33.6 m²
The area of the bottom base is 33.6 square meters.
Step 2.2: Calculate Area of the Top Base (A2)
Input Data:
- Length (L2) = 1.450 meters
- Width (b2) = 1.3 meters
Calculation:
A2 = 1.450 × 1.3 = 1.885 m²
The area of the top base is 1.885 square meters.
Step 2.3: Calculate the Geometric Mean (√(A1 × A2))
Calculation:
√(A1 × A2) = √(33.6 × 1.885) = √63.396 ≈ 7.967 m²
The geometric mean is 7.967 square meters.
Step 2.4: Substitute Values into the Formula
Substitute the values:
Vfrustum = (0.500 / 3) × (33.6 + 1.885 + 7.967)
Step 2.5: Simplify the Expression
Calculate the sum of areas:
33.6 + 1.885 + 7.967 = 43.452
Divide the height by 3:
0.500 / 3 = 0.1667
Multiply the results:
Vfrustum = 0.1667 × 43.452 = 7.242 m³
The volume of the trapezoidal frustum is 7.242 cubic meters.
Step 3: Total Volume of the Structure
The total volume is the sum of the rectangular base and trapezoidal frustum volumes:
Vtotal = Vrect + Vfrustum
Substitute the values:
Vtotal = 15.12 + 7.242
Final Calculation:
Vtotal = 22.362 m³
The total volume of the structure is 22.362 cubic meters.
Watch this video for a complete explanation by Er. Afroz on the Afroz Civil YouTube channel.
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