Surface To Volume Ratio Of Obtuse Edged Cuboid Given Cuboidal Edges Calculator

Surface To Volume Ratio Of Obtuse Edged Cuboid Formula:

\[ RA/V = \frac{2 \times \left( (l-(√2 \times w)) \times (w-(√2 \times w)) + (l-(√2 \times w)) \times (h-(√2 \times w)) + (w-(√2 \times w)) \times (h-(√2 \times w)) + 2 \times w \times ((l-(√2 \times w)) + (w-(√2 \times w)) + (h-(√2 \times w))) + 3 \times w^2 \right)}{(l-(√2 \times w)) \times (w-(√2 \times w)) \times (h-(√2 \times w)) + √2 \times w \times ((l-(√2 \times w)) \times (w-(√2 \times w)) + (l-(√2 \times w)) \times (h-(√2 \times w)) + (w-(√2 \times w)) \times (h-(√2 \times w))) + w^2 \times ((l-(√2 \times w)) + (w-(√2 \times w)) + (h-(√2 \times w))) + \left( \frac{4}{3 \times √2} \right) \times w^3} \]

Cuboidal Length of Obtuse Edged Cuboid:

Cuboidal Width of Obtuse Edged Cuboid:

Cuboidal Height of Obtuse Edged Cuboid:

Cut Width of Obtuse Edged Cuboid:

Surface To Volume Ratio Of Obtuse Edged Cuboid:

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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 its edges regularly cut off. This geometric shape is formed by removing triangular portions from the edges of a standard cuboid.

2. How Does the Calculator Work?

The calculator uses the complex formula:

Where:

\( l \) — Cuboidal Length (m)
\( w \) — Cuboidal Width (m)
\( h \) — Cuboidal Height (m)
\( w \) — Cut Width (m)
\( √2 \) — Square root of 2 (approximately 1.4142)

Explanation: The formula accounts for the reduced dimensions after edge cutting and calculates both the surface area and volume of the resulting complex polyhedron.

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 processes where the relationship between surface area and volume affects physical properties.

4. Using the Calculator

Tips: Enter all dimensions in meters. The cut width must be less than or equal to half the smallest dimension to ensure valid geometry. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is an obtuse edged cuboid?
A: An obtuse edged cuboid is a geometric shape formed by regularly cutting off the edges of a standard cuboid, creating triangular faces at each original edge.

Q2: Why is the surface to volume ratio important?
A: This ratio is critical in many physical phenomena where surface interactions dominate, such as heat dissipation, chemical reactivity, and biological processes like nutrient absorption.

Q3: What are typical values for this ratio?
A: The ratio varies significantly based on dimensions. Smaller objects generally have higher surface to volume ratios. Values typically range from 0.1 to 10 m⁻¹ for practical applications.

Q4: Are there limitations to this calculation?
A: The formula assumes perfect geometric cuts and may not account for manufacturing tolerances or irregular cuts. It's most accurate for mathematically perfect obtuse edged cuboids.

Q5: How does cut width affect the ratio?
A: Increasing cut width generally increases the surface to volume ratio as it creates additional triangular faces while reducing the overall volume more significantly than the surface area.