Total Surface Area Of Hollow Frustum Calculator

Formula Used:

\[ TSA = \frac{n}{4}(S_{Long Outer} + S_{Short Outer}) \sqrt{(\cot(\frac{\pi}{n}))^2(S_{Long Outer} - S_{Short Outer})^2 + 4h^2} + \frac{n}{4}(S_{Long Inner} + S_{Short Inner}) \sqrt{(\cot(\frac{\pi}{n}))^2(S_{Long Inner} - S_{Short Inner})^2 + 4h^2} + \frac{n(S_{Long Outer}^2 - S_{Long Inner}^2)}{4\tan(\frac{\pi}{n})} + \frac{n(S_{Short Outer}^2 - S_{Short Inner}^2)}{4\tan(\frac{\pi}{n})} \]

Number of Base Vertices (n):

Long Outer Side (S_{Long Outer}):

Short Outer Side (S_{Short Outer}):

Height (h):

Long Inner Side (S_{Long Inner}):

Short Inner Side (S_{Short Inner}):

Total Surface Area (TSA):

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1. What is the Total Surface Area of Hollow Frustum?

The Total Surface Area of a Hollow Frustum is the total quantity of plane occupied by the surface of the entire hollow frustum, including both inner and outer surfaces. It represents the complete surface area of this three-dimensional geometric shape.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

\( n \) — Number of base vertices
\( S_{Long Outer} \) — Long outer side length (m)
\( S_{Short Outer} \) — Short outer side length (m)
\( h \) — Height of the frustum (m)
\( S_{Long Inner} \) — Long inner side length (m)
\( S_{Short Inner} \) — Short inner side length (m)

Explanation: The formula calculates the total surface area by summing the lateral surface areas of both outer and inner surfaces, plus the area differences between outer and inner bases.

3. Importance of TSA Calculation

Details: Calculating the total surface area is crucial for various engineering and architectural applications, including material estimation, structural analysis, and cost calculations for hollow frustum-shaped objects.

4. Using the Calculator

Tips: Enter the number of base vertices (minimum 3), all side lengths in meters, and height in meters. All values must be positive numbers with appropriate relationships (outer sides should be larger than corresponding inner sides).

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow frustum?
A: A hollow frustum is a three-dimensional geometric shape formed by cutting the top off a pyramid or cone, creating a hollow interior with similar but smaller cross-sections.

Q2: Why are there both long and short sides?
A: The hollow frustum has different side lengths for the outer and inner surfaces at both base and top levels, accounting for the tapered hollow structure.

Q3: What units should I use for measurements?
A: The calculator uses meters for all length measurements, but you can use any consistent unit system as long as all inputs use the same units.

Q4: Are there any limitations to this formula?
A: This formula assumes regular polygonal bases and requires that inner dimensions are properly nested within outer dimensions to form a valid hollow frustum.

Q5: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal inputs with up to 4 decimal places precision for accurate calculations.