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:

1. Part-1: Truncated Pyramid

1. 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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