Tremie hopper is used to pour concrete into the pile foundation.

Let us now calculate the volume of the tremie hopper for the below-given drawing.

**three parts**as shown below.

**Part-1:**

__Given data__

Diameter = d =1000mm.=1m.

Height = h = 70mm.= 0.07m.

Shape **ðŸ‘‰** cylinder.

**The volume of part-1 **

= [Ï€ ×( d2)/4 × h ]

= [ 3.142 × (12 ) /4 × 0.07]

= [3.142 × 0.25 × 0.07]

=**0.055 cum.**

**Part-2**

The volume of the part-2 is calculated by the formula

= [ (h ÷ 3 ) ×{ A1+A2 + √A1× A2 }]

__Given data:__

Height = h = 550mm.=0.55m

Diameter of the top surface d1 = 1000mm.=1m.

Diameter of the bottom surface d2 = 200mm.=0.2m

Shape **ðŸ‘‰** frustum of a cone.

First, we will calculate the area A1 & A2

A1 = [( Ï€ × d12) ÷ 4]

= [( 3.142 × 12) ÷ 4]

= [3.412 ÷ 4]

= **0.7855 sqm.**

A2= [( Ï€ × d22) ÷ 4]

= [( 3.142 × 0.22) ÷ 4]

= [0.12568 ÷ 4]

=** 0.03142 sqm.**

**The volume of part-2**

= [ (h ÷ 3 ) ×{ A1+A2 + √A1× A2 }]

= [ (0.55 ÷ 3 ) ×{ 0.7855+0.03142 + √0.7855× 0.03142 }]

= [ (0.1833) ×{ 0.8169 + √0.02468 }]

= [ (0.1833) ×{ 0.8169 + 0.1571}]

=[ 0.1833 × 0.974]

=**0.178 cu m.**

= 6.3 cu ft.

**Part-3:**

__Given data__

Diameter = d3 =200mm.=0.2m.

Height = h = 150mm.= 0.15m.

Shape **ðŸ‘‰** cylinder.

**The volume of part-3 **

= [Ï€ ×( d32)/4 × h ]

= [ 3.142 × (0.22 ) /4 × 0.15]

= [3.142 × 0.01 × 0.15]

=**0.0047 cum.**

**Now, the total volume of tremie hopper**

= [vol.of part-1 + vol. of part-2 + vol. of part-3]

= [0.055 + 0.178 + 0.0047]

=**0.2377 cum.**

To calculate the volume of concrete in a hopper, we only consider the volume of the frustum ( part-2) of the tremie hopper.

So, **the concrete volume of the hopper** = **0.178 cum.**

**Note:**

1. Part -1 contains a hanging rod for lifting the hopper. So, we won't fill the concrete in part-1.

2. Part-3 is attached with a tremie pipe with a locking system. So, concrete is not filled in part-3.

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