Surface To Volume Ratio Of Hollow Cuboid Given Inner And Outer Breadth Calculator

Surface to Volume Ratio of Hollow Cuboid Formula:

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

Height of Hollow Cuboid:

Outer Breadth of Hollow Cuboid:

Outer Length of Hollow Cuboid:

Inner Breadth of Hollow Cuboid:

Surface to Volume Ratio:

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1. What is Surface to Volume Ratio of Hollow Cuboid?

The Surface to Volume Ratio of a Hollow Cuboid is defined as the numerical ratio of the total surface area of the Hollow Cuboid to the volume of the Hollow Cuboid. It's an important parameter in engineering and material science that indicates how much surface area is available per unit volume.

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: This formula calculates the ratio of surface area to volume for a hollow cuboid with given dimensions, accounting for both outer and inner surfaces.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in heat transfer applications, chemical reactions, and structural design. Higher ratios indicate more surface area relative to volume, which is important in applications like heat exchangers, catalysts, and packaging materials.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure that Outer Breadth is greater than Inner Breadth. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: All dimensions should be in consistent units (preferably meters). The result will be in reciprocal meters (m⁻¹).

Q2: Why is the surface to volume ratio important?
A: It's critical in many engineering applications including heat transfer efficiency, reaction rates in chemical processes, and material strength-to-weight ratios.

Q3: What if my inner breadth is larger than outer breadth?
A: The calculator requires that outer breadth must be greater than inner breadth for a valid hollow cuboid geometry.

Q4: Can this calculator handle different units?
A: The calculator expects all inputs in the same units. You can use any unit system as long as it's consistent, but the result will be in reciprocal of that unit.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the formula. Accuracy depends on the precision of your input measurements.