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Volume of Cone Frustum with a Core

vCalc Reviewed
Last modified by
on
May 8, 2024, 4:18:36 PM
Created by
on
Aug 12, 2014, 4:55:42 PM
V=13⋅π⋅h(a2+a⋅b+b2)-h⋅π⋅b2
(a)cone bottom radius
(b)core radius
(h)height
Tags
Volume Euclidean Geometry (3D) frustum cone Cored Verified
UUID
7ea93113-2241-11e4-b7aa-bc764e2038f2

The Volume of Cone Frustum with a Core calculator computes the volume (displacement) of cone frustum that has a cylindrical core based on the dimensions.

INSTRUCTIONS: Choose units and enter the following:

  • (a) Outer Radius
  • (b) Inner Radius
  • (h) Height

Cored Cone Frustum Volume (V): The volume is returned in cubic centimeters.  However, these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The formula for the volume (light grey area) of a right circular cone with a frustum defined by base radius (a) and top radius (b) and height (h) in between where the cylindrical core (dark grey area) has been removed.  This formula is simply the volume of the frustum of a cone minus the volume of a cylinder that would inscribe it.  This shape, upside down, is often used measure the volume of a bevel taken off the top of a cylinder.

/attachments/7ea93113-2241-11e4-b7aa-bc764e2038f2/Conecoredfrustumvolume-illustration.png

Uses

The chamfer put on top of a cylinder of an engine is a common use of this shape.
This equation, Volume of Cone Frustum with a Core, references 2 pages
This equation, Volume of Cone Frustum with a Core, is used in 3 pages
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