The volume of concrete in a trapezoidal footing is calculated by dividing the footing into two parts as it consists of two different geometrical shapes:
- Part-1: Truncated Pyramid
- Part-2: Cuboid
The total volume of the trapezoidal footing is:
Total Volume = Volume of Truncated Pyramid + Volume of Cuboid
1. Volume of Cuboid (Part-2)
Given Data:
- Length (L) = 750 mm = 0.75 m
- Breadth (B) = 600 mm = 0.6 m
- Height (H) = 300 mm = 0.3 m
Formula:
Volume of Cuboid = L × B × H
= 0.75m × 0.6m × 0.3m = 0.135m³
2. Volume of Truncated Pyramid (Part-1)
Given Data:
- Base Surface Length (L) = 750 mm = 0.75 m
- Base Surface Breadth (B) = 600 mm = 0.6 m
- Top Surface Length (l) = 450 mm = 0.45 m
- Top Surface Breadth (b) = 300 mm = 0.3 m
- Height (h) = 200 mm = 0.2 m
Formula:
Volume of Truncated Pyramid
a1 = l × b = 0.45m × 0.3m =0.135m²
a2 = L × B = 0.75m × 0.6m = 0.45m²
Substitute the values:
= (1/3) × (0.135 + 0.45 + √(0.135 × 0.45)) × 0.2
= (1/3) × (0.585 + 0.2465) × 0.2
= (1/3) × 0.8315 × 0.2
= 0.0554 m³
Total Volume of Trapezoidal Footing
Total Volume = Volume of Cuboid + Volume of Truncated Pyramid
= 0.135 m³ + 0.0554 m³
= 0.1904 m³
Convert to cubic feet:
= 0.1904 × 35.315
= 6.725 cu ft
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