Total Surface Area Of Hollow Cuboid Given Inner And Outer Breadth Calculator

Total Surface Area of Hollow Cuboid Formula:

\[ TSA = 4 \times \left( (h \times b_{Outer}) + (h \times l_{Outer}) + \left( b_{Outer} \times \frac{b_{Outer} - b_{Inner}}{2} \right) + \left( l_{Outer} \times \frac{b_{Outer} - b_{Inner}}{2} \right) - \left( 2 \times \frac{b_{Outer} - b_{Inner}}{2} \times h \right) - \left( 2 \times \left( \frac{b_{Outer} - b_{Inner}}{2} \right)^2 \right) \right) \]

Height of Hollow Cuboid (h):

Outer Breadth of Hollow Cuboid (bOuter):

Outer Length of Hollow Cuboid (lOuter):

Inner Breadth of Hollow Cuboid (bInner):

Total Surface Area of Hollow Cuboid (TSA):

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1. What is Total Surface Area of Hollow Cuboid?

The Total Surface Area of a Hollow Cuboid is defined as the total quantity of two dimensional space enclosed on the entire surface of the Hollow Cuboid. It includes both the outer and inner surfaces of the cuboid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( h \) — Height of Hollow Cuboid (m)
\( b_{Outer} \) — Outer Breadth of Hollow Cuboid (m)
\( l_{Outer} \) — Outer Length of Hollow Cuboid (m)
\( b_{Inner} \) — Inner Breadth of Hollow Cuboid (m)

Explanation: The formula accounts for all surfaces of the hollow cuboid, including both outer and inner faces, and subtracts the overlapping areas.

3. Importance of TSA Calculation

Details: Calculating the total surface area is crucial for determining material requirements, cost estimation, and structural analysis in construction and manufacturing applications involving hollow cuboidal structures.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure the outer breadth is greater than the inner breadth. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow cuboid?
A: A hollow cuboid is a three-dimensional shape with a cuboidal outer surface and a smaller cuboidal cavity inside, creating a hollow space.

Q2: Why is the formula so complex?
A: The formula accounts for all six faces of the outer cuboid, subtracts the inner hollow space, and adds the inner surfaces, resulting in a comprehensive calculation.

Q3: What are the units of measurement?
A: The calculator uses meters for all inputs, and the result is in square meters (m²).

Q4: Can this calculator handle different units?
A: No, all inputs must be in the same units (meters). Convert other units to meters before calculation.

Q5: What if the inner breadth is larger than the outer breadth?
A: This is physically impossible. The calculator will show an error if the inner breadth exceeds the outer breadth.