Let us calculate the volume of concrete in a trapezoidal footing as shown below.

The volume of the trapezoidal footing is calculated into 2 parts as it is made of two different shapes.

**Part-1**of the footing is known as a

__( as shown below )__

**truncated pyramid****part 2**of the footing is known as

**( as shown below )**

__cuboid__**The volume of the trapezoidal footing **

= [ (volume of the truncated pyramid ) + ( volume of the cuboid.) ]

= [ ( 1/3(a1 +a2 + √ a1 × a2 ) × h ) + ( L × B × H ) ]

Here,

a1 = top surface area of truncated pyramid ( part-1 )

= l × b

a 2 = base surface area of a truncated pyramid ( part-1 )

= L × B

Now, for the calculation purpose, let us redraw the above drawings with mathematical dimensions.

**a. The volume of the cuboid ( part-2 ) :**

Cuboid |

__Given data :__Length L = 750mm.

Breadth B = 600mm.

Height H = 300 mm.

**The volume of the cuboid **

= [L × B × H]

= [750mm × 600mm × 300mm]

= [0.75 m × 0.6m × 0.3m]

=**0.135 cum.**

**b. The volume of the truncated pyramid ( part-1 ) :**

__ Given data :__

Base surface length L = 750mm ( same as cuboid )

Base surface breadth B = 600 mm. ( same as cuboid )

Top surface length l = 450 mm

Top surface breadth b = 300mm.

Height h = 200mm.

**The volume of the truncated pyramid (part-1 )**

= [1/3(a1 +a2 + √ a1 × a2 ) × h]

Here,

**a1** = l × b

= 450mm × 300mm

= 0.45 m × 0.3 m

= **0.135 sqm.**

**a2** = L × B

= 750 mm × 600mm

= 0.75m × 0.6 m

= **0.45 sqm.**

The volume of the truncated pyramid ( part -1)

= 1/3 (0.135 sqm + 0.45 sqm + √ 0.135sqm × 0.45sqm ) × 0.2 m

= 1/3 ( 0.585 + √ 0.06075 ) × 0.2

= 1/3 (0.585 + 0.2465 ) × 0.2

= 1/3 × 0.8315 × 0.2

= **0.0554 cum.**

**The volume of concrete in trapezoidal footing**

= vol. of cuboid ( part-2 ) + vol. of truncated pyramid ( part-1 )

= 0.135 cum + 0.0554 cum

= **0.1904 cum.**

=**6.725 cu ft**. ( 1 cu ft = 35.315 cum )

**Thank you for going through these calculation steps❤. Have a good day ðŸ˜„.**

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