Surface To Volume Ratio Of Obtuse Edged Cuboid Calculator

Surface To Volume Ratio Of Obtuse Edged Cuboid Formula:

\[ RA/V = \frac{2 \times ((l_{Inner} \times w_{Inner}) + (w_{Inner} \times h_{Inner}) + (h_{Inner} \times l_{Inner}) + ((2 \times w_{Cut}) \times (l_{Inner} + w_{Inner} + h_{Inner})) + (3 \times w_{Cut}^2))}{(l_{Inner} \times w_{Inner} \times h_{Inner}) + (\sqrt{2} \times w_{Cut} \times ((l_{Inner} \times w_{Inner}) + (w_{Inner} \times h_{Inner}) + (h_{Inner} \times l_{Inner}))) + ((w_{Cut}^2) \times (l_{Inner} + w_{Inner} + h_{Inner})) + ((\frac{4}{3 \times \sqrt{2}}) \times w_{Cut}^3)} \]

Inner Length of Obtuse Edged Cuboid:

Inner Width of Obtuse Edged Cuboid:

Inner Height of Obtuse Edged Cuboid:

Cut Width of Obtuse Edged Cuboid:

Surface To Volume Ratio:

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1. What is Surface To Volume Ratio Of Obtuse Edged Cuboid?

The Surface To Volume Ratio of an Obtuse Edged Cuboid is the numerical ratio of the total surface area to the volume of a cuboid with rounded edges. It represents how much surface area is available per unit volume of the shape.

2. How Does the Calculator Work?

The calculator uses the Surface To Volume Ratio 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)
\( w_{Cut} \) — Cut Width of Obtuse Edged Cuboid (m)

Explanation: The formula accounts for both the inner dimensions of the cuboid and the cut width that creates the obtuse edges, providing an accurate surface to volume ratio calculation.

3. Importance of Surface To Volume Ratio Calculation

Details: Surface to volume ratio is crucial in various engineering and scientific applications, including heat transfer analysis, chemical reaction rates, material science, and biological systems where surface area affects processes like diffusion and absorption.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive numbers greater than zero. The cut width should be less than half the smallest dimension of the inner cuboid for physically meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What is an obtuse edged cuboid?
A: An obtuse edged cuboid is a three-dimensional shape formed by cutting off the edges of a regular cuboid, creating rounded or beveled edges instead of sharp corners.

Q2: Why is surface to volume ratio important?
A: Surface to volume ratio affects many physical and chemical properties, including heat dissipation, reaction rates, strength-to-weight ratios, and biological functions like nutrient absorption.

Q3: What are typical values for surface to volume ratio?
A: Values vary widely depending on dimensions. Smaller objects generally have higher surface to volume ratios. For cuboids, ratios typically range from 0.1 to 10 m⁻¹ or more.

Q4: How does cut width affect the surface to volume ratio?
A: Increasing cut width generally increases the surface area relative to volume, resulting in a higher surface to volume ratio, up to a certain point.

Q5: Can this calculator be used for engineering applications?
A: Yes, this calculator provides accurate surface to volume ratios that can be used in various engineering calculations involving heat transfer, fluid dynamics, and structural design.