Geometry

Truncated Cone Volume Calculator

Easily calculate the volume of a truncated cone (frustum) online using our free calculator. Input top radius, bottom radius, and height to find the volume. Visualize the frustum in 3D and copy the formula and result.

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3D Visualization

Formula

$$V = \frac13 \pi h (r_1^2 + r_1 r_2 + r_2^2)$$

What is a Truncated Cone (Frustum)?

A truncated cone, also known as a frustum, is the part of a cone that remains after its top portion has been cut off by a plane parallel to the base. Imagine taking a cone and slicing off the top in a straight, horizontal cut – what's left is a frustum. It has two circular bases of different radii and a slanted side surface.

Formula for Volume

The volume (V) of a frustum is calculated using the formula: $$V = \frac13 \pi h (r_1^2 + r_1 r_2 + r_2^2)$$ where:

  • $$r_1$$ is the radius of the top base
  • $$r_2$$ is the radius of the bottom base
  • $$h$$ is the height of the frustum (the perpendicular distance between the bases)

Uses of Truncated Cone Volume Calculator

This calculator is useful in various fields such as:

  • Engineering: Calculating the volume of components like buckets, lampshades, or architectural structures.
  • Construction: Estimating the amount of material needed for frustum-shaped structures.
  • Mathematics Education: Learning and verifying volume calculations in geometry.
  • Everyday Life: Calculating the capacity of containers that are frustum-shaped.

Learn more about truncated cones on Wikipedia.

Frequently Asked Questions

What is the Truncated Cone Volume Calculator?
The Truncated Cone Volume Calculator is an online Geometry calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the Truncated Cone Volume Calculator?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.
Can I use the Truncated Cone Volume Calculator for professional Geometry projects?
Yes. The math behind it is standard Geometry, so the results are reliable for professional use. That said, always double-check that your inputs are in the right format before relying on the output.
Why use the Truncated Cone Volume Calculator instead of calculating by hand?
Manual calculation is slow and error-prone, especially with multiple steps. This tool does the arithmetic for you and shows each step, so you can catch mistakes before they carry forward.
How do I format my inputs for the Truncated Cone Volume Calculator?
Type your numbers into the input fields. Leave out units and symbols unless a field specifically asks for them. The solver handles the rest.

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