# Some useful tips to determine the concrete quantity of hopper for piling

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In this civil engineering tutorial, you will learn the process for finding out the quantity of concrete in a average sized hopper that is required for piling in construction site.

The dimensions of the hopper are as follow :-

The shapes of the upper and lower portions of a hopper are cylindrical whereas the shape of the middle portion is frustum.

The diameter of the upper portion is taken as 1200 mm or 1.2 meter. The diameter of the lower portion is taken as 125 mm. The height of the cylindrical upper portion is taken as 70 mm and the height of the cylindrical lower portion is taken as 125 mm. The height of the middle frustum section is taken as 600 mm.

The upper cylindrical portion is considered as part 1. The middle frustum portion is considered as part 2 and the lower cylindrical portion is considered as part 3.

Initially, the volume of part 1 should be determined with the following formula :-

Diameter = 1.2 m; radius = 0.6 m; height = 0.070 m

After putting all the values, we get the following :-

3.14 x 0.6 x 0.6 x 0.070= 0.0791 cubic meter

Now determine the volume of part 2 (frustum) with following formula :-

Top diameter = 1.2 m; Radius (R) = 0.6 m; r = 0.0625 m

### Also Read: How to compute the quantity for cement, sand and aggregate for a concrete column

Bottom diameter = 0.125 m

Volume = πh / 3 (R^{2} + Rr + r^{2})

Here R = Radius of the top portion

Rr = Radius of the top portion & bottom portion

After putting the values, we get the following result :-

= 3.14 x 0.6 / 3 [(0.6)^{2} + (0.6 x 0.0625) + (0.0625)^{2}] = 0.2521 cubic meter

Now, it is required to determine the volume of part 3 with the following formula :-

Bottom diameter = 125 mm or 0.125 m; Radius (R) = 0.0625 m (0.125/2); Height = 120 mm = 0.12 m

Volume = πr^{2}h

After putting all the values, we get the following results :-

= 3.14 x 0.0625 x 0.0625 x 0.12 = 0.0015 cum

After summing all the portions, we get 0.333 cubic meter

So, total concrete volume of the hopper = 0.333 cubic meter

To get more details, go through the following video tutorial.

Video Source: L & T - Learning Technology

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