Volume of Hollow Frustum Calculator

Volume of Hollow Frustum Formula:

\[ V = \frac{h}{3} \times \left( \frac{n \times (S_{\text{Long Outer}}^2 + S_{\text{Short Outer}}^2)}{4 \times \tan(\pi/n)} + \frac{n \times S_{\text{Long Outer}} \times S_{\text{Short Outer}}}{4 \times \tan(\pi/n)} - \frac{n \times (S_{\text{Long Inner}}^2 + S_{\text{Short Inner}}^2)}{4 \times \tan(\pi/n)} - \frac{n \times S_{\text{Long Inner}} \times S_{\text{Short Inner}}}{4 \times \tan(\pi/n)} \right) \]

Height of Hollow Frustum:

Number of Base Vertices:

Long Outer Side:

Short Outer Side:

Long Inner Side:

Short Inner Side:

Volume of Hollow Frustum:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Volume of Hollow Frustum?

A hollow frustum is a three-dimensional geometric shape that resembles a truncated pyramid with a hollow interior. It has two parallel bases (top and bottom) that are regular polygons with different side lengths, and the interior is also hollow with similar polygonal shapes.

2. How Does the Calculator Work?

The calculator uses the volume formula:

Where:

\( V \) — Volume of hollow frustum (m³)
\( h \) — Height of hollow frustum (m)
\( n \) — Number of base vertices
\( S_{\text{Long Outer}} \) — Long outer side length (m)
\( S_{\text{Short Outer}} \) — Short outer side length (m)
\( S_{\text{Long Inner}} \) — Long inner side length (m)
\( S_{\text{Short Inner}} \) — Short inner side length (m)
\( \pi \) — Mathematical constant pi (≈3.14159)
\( \tan \) — Tangent trigonometric function

Explanation: The formula calculates the volume by finding the difference between the outer frustum volume and the inner hollow portion volume.

3. Importance of Volume Calculation

Details: Calculating the volume of hollow frustums is important in various engineering and architectural applications, particularly in construction, manufacturing, and design where such shapes are used in structures, containers, or mechanical components.

4. Using the Calculator

Tips: Enter all measurements in meters. The number of vertices must be at least 3 (triangle or more sides). All side lengths must be positive values.

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow frustum?
A: A hollow frustum is a truncated pyramid-like shape with a hollow interior, having two parallel polygonal bases of different sizes.

Q2: What are common applications of hollow frustums?
A: They are commonly used in architecture (building designs), engineering (containers, pipes), and manufacturing (molds, structural components).

Q3: Why is the tangent function used in the formula?
A: The tangent function helps calculate the area of regular polygons, which is necessary for determining the cross-sectional areas of the frustum.

Q4: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurements to meters before inputting them.

Q5: What is the minimum number of vertices required?
A: The minimum is 3 vertices, which creates a triangular hollow frustum. Higher numbers create shapes with more sides (square, pentagon, etc.).