### HOW TO CALCULATE CONCRETE VOLUME OF TRAPEZOIDAL FOOTING/ SLOPED FOOTING

How to calculate concrete volume of trapezoidal footing

• A trapezoid is a combination of a cuboid and a truncated pyramid.
• Trapezoidal footing = Volume of cuboid +  volume of truncated pyramid.
So to calculate the volume of trapezoidal footing we need to calculate the volume of a cuboid and a truncated pyramid.

1. Volume of rectangular cuboid
= Length X Breadth X Height

2. Volume of truncated pyramid
= h/3 { A1 + A2 + √(A1 X A2)}
Where,
h = height of truncated pyramid
A1 = Area of base of truncated pyramid
A2 = Area of top of truncated pyramid

Let take an example of Trapezoidal footing to understand it well.

Here is a figure of rectangular trapezoidal footing.

As per data given in the figure, detailed calculation of the volume of trapezoidal footing are given below.

1. Volume of rectangular cuboid
= 1.5 X 2.0 X 0.3
= 0.9 cu.m

2. Volume of truncated pyramid
= h/3 {A1+A2+√(A1 X A2)}
Where,
A1 = 1.5 X 2.0 = 3 sq.m
A2 = [0.3 + (2x0.1)] X [0.45+(2x0.1)]
= 0.325 sq.m

= 0.6/3 ( 3+ 0.325 + √ 3x 0.325)
= 0.862 cu.m

Total volume of trapezoidal footing
= Volume of cuboid + Volume of truncated pyramid
= 0.9 + 0.862
= 1.762 cu.m

So we have a total volume of trapezoidal footing is 1.762 cu.m