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Cone Frustum Volume

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Last modified by
on
Dec 23, 2024, 1:44:40 PM
Created by
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Jan 4, 2014, 7:06:03 PM
V=13⋅π⋅h(a2+a⋅b+b2)
(a)top radius
(b)bottom radius
(h)height
Tags
Volume Euclidean Geometry (3D) vSample frustum cone 3D Verified
UUID
e6cc9bde-da27-11e2-8e97-bc764e04d25f

The Volume of the Frustum of a Cone calculator computes the volume of a frustum (slice) of a cone based on the top radius (a), bottom radius (b) and height (h) in between. 

INSTRUCTION: Choose units and enter the following:

  • (a) - radius of top surface
  • (b) - radius of bottom surface
  • (h) - height in between top and bottom

Volume of the Cone Section (V):  The calculator computes the volume (V) in cubic meters (m3).  However this can be automatically converted to many other volume units (e.g. gallons or cubic feet) via the pull-down menu.  

The Math

The frustum of a cone is a section of a cone also known as a truncated cone. The frustum of a cone is created by parallel planes that go through the cone and are normal (perpendicular) to the center axis of the cone.  The shape of the top and bottom are perfect circles whose centers are directly aligned.  The planes are separated by the height (h). The formula for the Volume of the Frustum of a cone is as follows:

         V = 1/3 • π • h(a2+a•b+b2)    

where:/attachments/e6cc9bde-da27-11e2-8e97-bc764e04d25f/ConeFrustumVolume-illustration.png 

Cone Calculators

  1. Cone Surface Area based on cone height and cone base radius
  2. Cone Volume based on cone height and cone base radius
  3. Cone Mass or Weight as a function of the volume and mean density
  4. Cone Frustum Surface Area based on the two heights and two radii
  5. Cone Frustum Volume based on the two heights and two radii 
  6. Cone Frustum Weight or Mass based on the cone frustum volume and mean density
  7. Cone Shell Volume a.k.a. hollow cone volume
  8. Cone Shell Mass or Weight a.k.a. hollow cone mass
  9. Moment of inertia of a cone shaped object based on mass and rotation axis
  10. Moment of inertia of a cone shaped object based on mass and distance to apex (rotation around apex)
  11. Compute the total surface are of the frustum of a cone:  This includes the top and bottom surfaces.
  12. Compute the lateral surface area (using L) of the frustum of a cone.
  13. Cone Frustum Volume from Angle
  14. Cone Frustum Height from Volume and Outer Side Angle: Computes height based on volume, small radius and outer side angle.
  15. Cone Frustum Height from Volume and Inner Side Angle: Computes height based on volume, small radius and inner side angle.

See Also

Volume is a three dimensional measurement of the amount of space taken up by an object.  Volume units are cubic measurements for solid objects such as cubic inches and cubic meters.  Fluids have separate volume units such as liters, fluid ounces, cups, gallons, and barrel. 

The volume of an object can measured by the liquid it displaces or be calculated by measuring its dimensions and applying those dimensions to a formula describing its shape.  Many such calculations are available in the following list of calculators. 

In many cases, the calculators are for a column with a geometric shaped base and vertical sides.  One basic formula for volume is area times a Height when the volume has vertical sides.

Volume Calculators

Reference

  • Equation 4.42 Spiegel, Murray R. "Chapter 4." Mathematical Handbook of Formulas and Tables. New York: McGraw-Hill, 1968. N. pag. Print.
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