Surface To Volume Ratio Of Parallelepiped Given Perimeter, Side A And Side C Calculator

Surface To Volume Ratio Of Parallelepiped Formula:

\[ RA/V = \frac{2 \times ((S_a \times (P/4-S_a-S_c) \times \sin(\gamma)) + (S_a \times S_c \times \sin(\beta)) + ((P/4-S_a-S_c) \times S_c \times \sin(\alpha)))}{S_a \times (P/4-S_a-S_c) \times S_c \times \sqrt{1 + (2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma)) - (\cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2)}} \]

Side A of Parallelepiped (S_a):

Perimeter of Parallelepiped (P):

Side C of Parallelepiped (S_c):

Angle Alpha (α):

rad

Angle Beta (β):

rad

Angle Gamma (γ):

rad

Surface to Volume Ratio (RA/V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Surface to Volume Ratio of Parallelepiped?

The Surface to Volume Ratio of a Parallelepiped is the numerical ratio of the total surface area to the volume of the parallelepiped. 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:

\( S_a \) — Side A of Parallelepiped (m)
\( P \) — Perimeter of Parallelepiped (m)
\( S_c \) — Side C of Parallelepiped (m)
\( \alpha \) — Angle Alpha between sides B and C (rad)
\( \beta \) — Angle Beta between sides A and C (rad)
\( \gamma \) — Angle Gamma between sides A and B (rad)

Explanation: The formula calculates the surface to volume ratio by considering all three pairs of sides and their respective angles in the parallelepiped structure.

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 in three-dimensional objects.

4. Using the Calculator

Tips: Enter all dimensions in meters and angles in radians. Ensure all values are positive and valid. The perimeter should be greater than 4 times the sum of side A and side C.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms. It's the 3D equivalent of a parallelogram.

Q2: Why is the surface to volume ratio important?
A: This ratio is critical in many physical and chemical processes where surface interactions are important, such as catalysis, heat transfer, and fluid dynamics.

Q3: How do I convert degrees to radians?
A: Multiply degrees by π/180. For example, 90° = 90 × π/180 = π/2 radians ≈ 1.5708 radians.

Q4: What are typical values for surface to volume ratio?
A: The ratio depends on the specific dimensions and angles. Smaller objects generally have higher surface to volume ratios than larger objects of the same shape.

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