Truncated Cone Volume Calculator
Easily calculate the volume of a truncated cone (frustum) with our interactive tool. Enter the top radius ($$r_1$$), bottom radius ($$r_2$$), and height ($$h$$) to get the volume and visualize the 3D shape.
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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.