Side A Of Parallelepiped Calculator

Formula Used:

\[ Sa = \frac{V}{Sb \times Sc \times \sqrt{1 + (2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma)) - (\cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2)}} \]

Volume of Parallelepiped:

m³

Side B of Parallelepiped:

Side C of Parallelepiped:

Angle Alpha of Parallelepiped:

Angle Beta of Parallelepiped:

Angle Gamma of Parallelepiped:

Side A of Parallelepiped:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Side A of Parallelepiped?

Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped. It is calculated using the volume and the other two sides along with the angles between them.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Sa = \frac{V}{Sb \times Sc \times \sqrt{1 + (2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma)) - (\cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2)}} \]

Where:

\( Sa \) — Side A of Parallelepiped (m)
\( V \) — Volume of Parallelepiped (m³)
\( Sb \) — Side B of Parallelepiped (m)
\( Sc \) — Side C of Parallelepiped (m)
\( \alpha \) — Angle Alpha of Parallelepiped (radians)
\( \beta \) — Angle Beta of Parallelepiped (radians)
\( \gamma \) — Angle Gamma of Parallelepiped (radians)

Explanation: This formula calculates the length of side A based on the volume of the parallelepiped and the lengths of the other two sides, considering the angles between them.

3. Importance of Side A Calculation

Details: Calculating side A is important in geometry and engineering applications where the dimensions of a parallelepiped need to be determined from known volume and other parameters.

4. Using the Calculator

Tips: Enter volume in cubic meters, side lengths in meters, and angles in degrees. All values must be positive and angles between 0-180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure formed by six parallelograms. It has three sets of parallel faces.

Q2: How are the angles defined in a parallelepiped?
A: The angles α, β, and γ are the angles between sides at any vertex: α between sides B and C, β between sides A and C, and γ between sides A and B.

Q3: What units should I use for the inputs?
A: Use consistent units - meters for lengths, cubic meters for volume, and degrees for angles. The calculator will convert angles to radians internally.

Q4: Can this formula be used for any parallelepiped?
A: Yes, this formula works for any parallelepiped where the volume and two adjacent sides with their angles are known.

Q5: What if I get a negative result or error?
A: This typically indicates invalid input values. Ensure all values are positive and angles are between 0-180 degrees. The expression under the square root must be positive.