Liquid Volume of a Frustum of a Cone

In summary, the person is looking for an equation to calculate the volume of a frustum of a cone, specifically for any level of liquid within the tank. The frustum is measured with a height of 6m and diameters of 5m and 3m, with the wider part towards the base. The suggested solution is to calculate the volume by subtracting the volume of the frustum above the liquid line from the volume of the frustum below the liquid line.
  • #1
labsean
1
0

Homework Statement


I have been searching online for help with this equation but have found nothing at this stage.

I am looking for an equation to satisfy the Volume of a Frustum of a cone. The liquid level is measured via a sensor located in the centre point, top circle(area) of the furstum. I am looking for a formula for, that any level of liquid within the tank, a volume will be given.


Homework Equations


the frustum is measured at: h=6m; D=5m and d=3m...note the frustum is bottom heavy(gets wider towards the base)


The Attempt at a Solution


My understanding of this is, that a Volume for any level of liquid = Volume of frustum above the liguid line - Volume of the frustum below the liquid line.

Thanks in advance, any help is greatly appriciated.


Sean
 
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  • #2
If I remember what a frustum is properly then you can make one large cone and subtract a smaller cone. (if you extend the sides of the smaller diameter to a point you would get a cone)
 

Related to Liquid Volume of a Frustum of a Cone

1. What is a frustum of a cone?

A frustum of a cone is a three-dimensional shape that is formed when the top of a cone is cut off by a plane parallel to its base.

2. How is the liquid volume of a frustum of a cone calculated?

The liquid volume of a frustum of a cone is calculated by using the formula V = (1/3) * π * h * (R^2 + Rr + r^2), where V is the volume, h is the height of the frustum, R is the radius of the base, and r is the radius of the top of the frustum.

3. Can the liquid volume of a frustum of a cone be greater than the volume of a full cone?

Yes, the liquid volume of a frustum of a cone can be greater than the volume of a full cone if the height of the frustum is shorter than the height of the full cone.

4. Is the liquid volume of a frustum of a cone affected by the shape of the top and bottom bases?

Yes, the liquid volume of a frustum of a cone is affected by the shape of the top and bottom bases. A frustum with a larger base will have a greater volume, while a frustum with a smaller base will have a smaller volume.

5. How is the liquid volume of a frustum of a cone used in real life?

The liquid volume of a frustum of a cone is used in various real-life applications such as in engineering, construction, and manufacturing industries. For example, it can be used to calculate the volume of liquid in a partially filled cone-shaped container or to determine the volume of a liquid storage tank with a conical shape.

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