Liquid Volume of a Frustum of a Cone

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SUMMARY

The volume of a frustum of a cone can be calculated using the formula V = (1/3)πh(R² + Rr + r²), where R is the radius of the top circle, r is the radius of the bottom circle, and h is the height of the frustum. In this discussion, the specific dimensions provided are h = 6m, D = 5m (top diameter), and d = 3m (bottom diameter), leading to R = 2.5m and r = 1.5m. To find the volume of liquid at any level, one must calculate the volume of the frustum above the liquid line and subtract the volume below it.

PREREQUISITES
  • Understanding of geometric shapes, specifically cones and frustums.
  • Familiarity with volume calculation formulas in geometry.
  • Basic knowledge of algebra for manipulating equations.
  • Ability to visualize three-dimensional shapes and their dimensions.
NEXT STEPS
  • Research the derivation of the frustum volume formula.
  • Learn how to apply calculus to find volumes of irregular shapes.
  • Explore practical applications of frustum volume calculations in engineering.
  • Study the use of sensors for liquid level measurement in tanks.
USEFUL FOR

Students studying geometry, engineers working with fluid dynamics, and anyone involved in designing or analyzing tanks and reservoirs.

labsean
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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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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)
 

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