Cone and Truncated Cone Volume Calculator

Select Shape:

Radius \( r \):

Height \( h \):

Base Radius \( R \):

Top Radius \( r \):

Depth \( h \):

Volume (cm³): Volume (in³): Volume (ft³): Volume (m³): Volume (L):

1. What is a Cone and Truncated Cone Volume Calculator?

Definition: This calculator computes the volume of a cone or a truncated cone (frustum) based on its dimensions. A cone is a solid with a circular base and a single vertex, while a truncated cone is a cone with its top cut off perpendicular to its height.

Purpose: Useful in geometry, engineering, and design for determining the volume of conical shapes, including applications like flower pots.

2. How Does the Calculator Work?

The calculations are based on the following formulas:

\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \] \[ V_{\text{truncated cone}} = \frac{1}{3} \pi \times \text{depth} \times (r^2 + r \times R + R^2) \]

Notes: A cone with a polygonal base is called a pyramid (see pyramid volume calculator). The truncated cone volume can also be found by subtracting the smaller cone volume from the larger cone volume.

Unit Conversions:

Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48) to cm
Volume: cm³ (direct), in³ (×0.0610237), ft³ (×0.0000353147), m³ (×0.000001), L (×0.001)

Explanation: All dimensions are converted to cm, the volume is calculated in cm³, and then converted to in³, ft³, m³, and L.

3. Importance of Cone and Truncated Cone Volume Calculation

Details: Calculating the volume of cones and truncated cones is essential in engineering (e.g., designing funnels, silos), horticulture (e.g., flower pots), and architecture.

4. Using the Calculator

Tips: Select the shape (Cone or Truncated Cone), then enter the required dimensions (radius and height for a cone; base radius, top radius, and depth for a truncated cone) in mm, cm, m, in, or ft (all must be >0). The result shows the volume in cm³, in³, ft³, m³, and L.

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