`V = f( "a" , "b" , "h" , "t" )`

Enter a value for all fields

The Volume of the Shell of a Cone (Hollow Cone) calculator computes the volume of the shell of a cone.  The volume is a function of the top radius (a), bottom radius (b), thickness (t) and height (h) in between. 

INSTRUCTION: Choose your length units (e.g. inches or meters) and enter the following:

• (a) Outer Radius of Top surface
• (b) Outer Radius of Bottom surface
• (h) Height between Top and Bottom
• (t) Thickness of Shell

Cone Shell Volume (V): The calculator computes the volume 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.  To compute the Weight of the Shell of a Cone, CLICK HERE.

The Math

Note: the frustum is created by parallel planes that go through the cone and are normal (perpendicular) to the center axis of the cone.  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)
 

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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.

See Also

• Frustum Calculator - Equations for volume, mass and surface areas for various frustums.
• Planter Calculator - Equations for home and garden planters.
• Volume Calculator - Volume equations for various geometric shapes
• Mass Weight Calculator - Equations for the mass and weight of objects based on their mean density and shape

The following table contains links to calculators that compute the volume of other shapes:

Other Volume Calculators
Various Shapes		Polygon Columns
Cube	Triangular Prism	Triangular
Box	Paraboloid	Quadrilateral
Cone	Polygon based Pyramid	Pentagon
Cone Frustum	Pyramid Frustum	Hexagon
Cylinder	Sphere	Heptagon
Slanted Cylinder	Sphere Cap	Octogon
Ellipsoid	Oblate Spheroid	Nonogon
Torus	Capsule	Decagon

Reference

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