Total Surface Area Of Hollow Cuboid Given Volume Calculator

Formula Used:

\[ TSA = 4 \times \left( \frac{V}{2 \times t \times (l_{outer} + b_{outer} - (2 \times t))} \times l_{outer} + \frac{V}{2 \times t \times (l_{outer} + b_{outer} - (2 \times t))} \times b_{outer} + (l_{outer} \times t) + (b_{outer} \times t) - \frac{V}{l_{outer} + b_{outer} - (2 \times t)} - (2 \times t^2) \right) \]

Volume of Hollow Cuboid (V):

m³

Thickness of Hollow Cuboid (t):

Outer Length of Hollow Cuboid (l_outer):

Outer Breadth of Hollow Cuboid (b_outer):

Total Surface Area of Hollow Cuboid (TSA):

Unit Converter ▲

Unit Converter ▼

From:	To:

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, including both inner and outer surfaces.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( TSA \) — Total Surface Area of Hollow Cuboid (m²)
\( V \) — Volume of Hollow Cuboid (m³)
\( t \) — Thickness of Hollow Cuboid (m)
\( l_{outer} \) — Outer Length of Hollow Cuboid (m)
\( b_{outer} \) — Outer Breadth of Hollow Cuboid (m)

Explanation: This formula calculates the total surface area by considering the volume and geometric properties of the hollow cuboid structure.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for various engineering applications, material estimation, heat transfer calculations, and structural design where hollow cuboidal structures are used.

4. Using the Calculator

Tips: Enter all values in meters and cubic meters. Ensure that thickness is less than half of the smaller outer dimension to maintain physical validity. 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 inner cavity, creating a hollow space inside.

Q2: Why is the formula so complex?
A: The complexity arises from accounting for both inner and outer surfaces, their interactions, and the volume constraint that relates all dimensions.

Q3: What are the units for the result?
A: The total surface area is calculated in square meters (m²), consistent with the input dimensions in meters.

Q4: Are there any limitations to this formula?
A: The formula assumes uniform thickness and requires that the inner cavity maintains the same proportions as the outer cuboid.

Q5: When might this calculation be used in real-world applications?
A: This calculation is useful in construction, packaging design, heat exchanger design, and any application involving hollow rectangular structures.