Total Surface Area of Truncated Cuboid Calculator

Total Surface Area of Truncated Cuboid Formula:

\[ TSA = l \times (h + w + h_{Short} + l_{e(Inclined)} + w_{Short}) + (2 \times h \times w) - ((h - h_{Short}) \times (w - w_{Short})) \]

Length of Truncated Cuboid (l):

Height of Truncated Cuboid (h):

Width of Truncated Cuboid (w):

Shortened Height of Truncated Cuboid (h_Short):

Inclined Edge of Truncated Cuboid (l_e(Inclined)):

Shortened Width of Truncated Cuboid (w_Short):

Total Surface Area of Truncated Cuboid (TSA):

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1. What is the Total Surface Area of Truncated Cuboid?

The Total Surface Area of a Truncated Cuboid refers to the total area of all the surfaces of a cuboid that has been truncated (cut) at one corner. It includes the areas of all faces: the base, top, sides, and the truncated surfaces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = l \times (h + w + h_{Short} + l_{e(Inclined)} + w_{Short}) + (2 \times h \times w) - ((h - h_{Short}) \times (w - w_{Short})) \]

Where:

\( l \) — Length of Truncated Cuboid (m)
\( h \) — Height of Truncated Cuboid (m)
\( w \) — Width of Truncated Cuboid (m)
\( h_{Short} \) — Shortened Height of Truncated Cuboid (m)
\( l_{e(Inclined)} \) — Inclined Edge of Truncated Cuboid (m)
\( w_{Short} \) — Shortened Width of Truncated Cuboid (m)

Explanation: The formula accounts for all surfaces of the truncated cuboid, including the main surfaces and the truncated section, providing the total surface area.

3. Importance of TSA Calculation

Details: Calculating the total surface area is crucial for applications such as material estimation, construction planning, packaging design, and any scenario where surface coverage needs to be determined.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive and valid. The shortened dimensions should be less than or equal to their respective full dimensions.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated cuboid?
A: A truncated cuboid is a cuboid that has been cut at one corner, resulting in a shape with a slanted surface instead of a right angle.

Q2: How is this different from a regular cuboid's surface area?
A: A truncated cuboid has additional surfaces from the truncated section, making its total surface area calculation more complex than a regular cuboid.

Q3: What are typical applications of this calculation?
A: This calculation is useful in architecture, manufacturing, packaging design, and any field dealing with irregular 3D shapes.

Q4: Are there any limitations to this formula?
A: This formula assumes specific truncation geometry. For different truncation patterns, alternative calculations may be needed.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert all measurements to meters before calculation.