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`M = [1/3 * pi * "h" ( "a" ^2+ "a" * "b" + "b" ^2)]* "mD" `

Enter a value for all fields

The **Weight of a Cone** calculator computes the mass (weight) of a right circular cone or cone frustum defined by a top radius (**a**) and base radius (**b**), height (**h**) in between, using the mean density (**mD**) and volume to calculate the mass of the object. The frustum of a cone is also known as a truncated cone.

**INSTRUCTIONS:** Choose units and enter the following:

- (
**a**) Top radius of the cone's frustum (see diagram) - (
**b**) Bottom radius of the cone's frustum (see diagram) - (
**h**) Height of the cone or cone section - (
**mD**) The mean density of the substance of the cone (CLICK HERE).

**Weight of a Cone (M):** The calculator computes the mass/weight of the cone in kilograms. However, this can be automatically converted to numerous other mass/weight units (e.g. pound, tons) via the pull-down menu. **Note:** For a complete cone, simple let the top radius (**a**) remain as zero.

For an instructional video (YouTube) click HERE.

The formula for the mass or weight of the frustum of a cone is:

`M = [1/3 * π * h(a^{2}+ a*b+ b^{2})]*ρ`

where:

- M = Mass or weight of frustum of cone
- a = upper radius
- b = radius of base
- h = height of frustum
- ρ = mean density of material in cone

This calculator first computes the Volume of the Frustum of a Cone (CLICK HERE), and then uses that volume with the mean density as follows:

The mean density (mD, μD or ρ) of many common substances, elements, liquids and materials can be found by clicking** HERE **(e.g. the μD_{(water)} is 1000.0 kg/m³).

- Surface Area: cone surface area based on cone height and cone base radius
- Volume: cone volume based on cone height and cone base radius
- Mass: cone mass or weight as a function of the volume and mean density
- Frustum Surface Area: cone frustum surface area based on the two heights and two radii
- Frustum Volume: cone frustum volume based on the two heights and two radii
- Frustum Mass: cone frustum weight or mass based on the cone frustum volume and mean density
- Shell Volume: cone shell volume a.k.a. hollow cone volume
- Shell Mass: cone shell mass or weight a.k.a. hollow cone mass.
- Compute the total surface are of the frustum of a cone: This includes the top and bottom surfaces.
- Compute the lateral surface area (using L) of the frustum of a cone.
- Volume of the frustum of a cone: ` V = 1/3⋅π⋅h(a^2+a⋅b+b^2)`
- Volume of a cone: ` V = 1/3⋅π⋅r^2⋅h`
- Weight of a cone: ` W = 1/3⋅π⋅r^2⋅h * muD`
- For other formulas related to the frustums of other shapes (e.g. pyramids of different sizes), see the Frustum Calculator.