Surface to Volume Ratio of Parallelepiped given Lateral Surface Area Calculator

Surface to Volume Ratio of Parallelepiped Formula:

\[ RA/V = \frac{LSA + 2 \times Sa \times Sc \times \sin(\angle\beta)}{\frac{LSA \times Sa \times Sc}{2 \times (Sa \times \sin(\angle\gamma) + Sc \times \sin(\angle\alpha))} \times \sqrt{1 + (2 \times \cos(\angle\alpha) \times \cos(\angle\beta) \times \cos(\angle\gamma)) - (\cos(\angle\alpha)^2 + \cos(\angle\beta)^2 + \cos(\angle\gamma)^2)}} \]

Lateral Surface Area of Parallelepiped (LSA):

m²

Side A of Parallelepiped (Sa):

Side C of Parallelepiped (Sc):

Angle Alpha of Parallelepiped:

rad

Angle Beta of Parallelepiped:

rad

Angle Gamma of Parallelepiped:

rad

Surface to Volume Ratio of Parallelepiped:

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1. What is Surface to Volume Ratio of Parallelepiped?

The Surface to Volume Ratio of Parallelepiped is the numerical ratio of the total surface area of a parallelepiped to its volume. It's an important geometric property that describes how much surface area is available per unit volume of the shape.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( LSA \) — Lateral Surface Area of Parallelepiped (m²)
\( Sa \) — Side A of Parallelepiped (m)
\( Sc \) — Side C of Parallelepiped (m)
\( \angle\alpha \) — Angle Alpha of Parallelepiped (radians)
\( \angle\beta \) — Angle Beta of Parallelepiped (radians)
\( \angle\gamma \) — Angle Gamma of Parallelepiped (radians)

Explanation: This formula calculates the surface to volume ratio by considering the lateral surface area, two sides of the parallelepiped, and the three angles between these sides.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and engineering. It helps determine properties like heat transfer efficiency, reaction rates, and structural strength of parallelepiped-shaped objects.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, square meters for area, and radians for angles). All values must be positive numbers within valid ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms. It's a polyhedron with parallelogram faces.

Q2: Why is the surface to volume ratio important?
A: This ratio is important in many scientific and engineering applications as it affects properties like heat dissipation, chemical reactivity, and structural efficiency.

Q3: How do I convert degrees to radians?
A: Multiply the degree value by π/180 (approximately 0.0174533) to convert to radians.

Q4: What are typical values for surface to volume ratio?
A: The value depends on the specific dimensions of the parallelepiped. Generally, smaller objects have higher surface to volume ratios.

Q5: Can this calculator be used for cubes and rectangular prisms?
A: Yes, since cubes and rectangular prisms are special cases of parallelepipeds where all angles are 90 degrees (π/2 radians).