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 (see diagram)
- (b) Bottom Radius (see diagram)
- (h) Height of 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 Math / Science
The formula for the mass or weight of the frustum of a cone is:
`M = [1/3 * π * h(a2+ a*b+ b2)]*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).
Cone Calculators:
- 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.