Total Surface Area Of Obtuse Edged Cuboid Given Inner Height And Cut Width Calculator

Formula Used:

\[ TSA = 2 \times ((l_{Inner} \times w_{Inner}) + (w_{Inner} \times h_{Inner}) + (h_{Inner} \times l_{Inner}) + ((2 \times \frac{(h_{Cuboid} - h_{Inner})}{\sqrt{2}}) \times (l_{Inner} + w_{Inner} + h_{Inner})) + (3 \times (w_{Cut})^2)) \]

Inner Length of Obtuse Edged Cuboid:

Inner Width of Obtuse Edged Cuboid:

Inner Height of Obtuse Edged Cuboid:

Cuboidal Height of Obtuse Edged Cuboid:

Cut Width of Obtuse Edged Cuboid:

Total Surface Area of Obtuse Edged Cuboid:

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1. What is the Total Surface Area of Obtuse Edged Cuboid?

The Total Surface Area of Obtuse Edged Cuboid is the total quantity of two dimensional space enclosed on the entire surface of the Obtuse Edged Cuboid. It accounts for both the inner surfaces and the additional surfaces created by cutting the edges.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( l_{Inner} \) — Inner Length of Obtuse Edged Cuboid (m)
\( w_{Inner} \) — Inner Width of Obtuse Edged Cuboid (m)
\( h_{Inner} \) — Inner Height of Obtuse Edged Cuboid (m)
\( h_{Cuboid} \) — Cuboidal Height of Obtuse Edged Cuboid (m)
\( w_{Cut} \) — Cut Width of Obtuse Edged Cuboid (m)

Explanation: The formula calculates the total surface area by considering the inner rectangular faces, the additional surfaces from edge cutting, and the corner surfaces created by the cut.

3. Importance of Surface Area Calculation

Details: Accurate surface area calculation is crucial for material estimation, heat transfer calculations, coating applications, and structural analysis in engineering and architectural designs involving obtuse edged cuboids.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive and the cuboidal height is greater than the inner height. The calculator provides precise results for engineering and mathematical applications.

5. Frequently Asked Questions (FAQ)

Q1: What is an obtuse edged cuboid?
A: An obtuse edged cuboid is a three-dimensional shape formed by regularly cutting off the edges of a standard cuboid, creating additional surfaces with obtuse angles.

Q2: Why is the square root of 2 used in the formula?
A: The square root of 2 appears because the edge cutting creates triangular surfaces with 45-degree angles, where the relationship between the cut dimensions involves the Pythagorean theorem.

Q3: What are the practical applications of this calculation?
A: This calculation is used in manufacturing, packaging design, architectural elements, and any application where materials with chamfered or beveled edges are used.

Q4: Can this formula be used for acute edged cuboids?
A: No, this specific formula is designed for obtuse edged cuboids. Acute edged cuboids would require a different mathematical approach.

Q5: How accurate is this calculation for real-world applications?
A: The calculation provides theoretical accuracy. For practical applications, material thickness, manufacturing tolerances, and other factors may need to be considered.