Volume Of Parallelepiped Given Total Surface Area And Lateral Surface Area Calculator

Volume Of Parallelepiped Formula:

\[ V = \frac{1}{2} \times \frac{(TSA - LSA)}{\sin(\beta)} \times S_b \times \sqrt{1 + (2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma)) - (\cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2)} \]

Total Surface Area Of Parallelepiped (TSA):

m²

Lateral Surface Area Of Parallelepiped (LSA):

m²

Angle Beta Of Parallelepiped (β):

Side B Of Parallelepiped (S_b):

Angle Alpha Of Parallelepiped (α):

Angle Gamma Of Parallelepiped (γ):

Volume Of Parallelepiped (V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Is The Volume Of Parallelepiped Formula?

The volume of a parallelepiped can be calculated using the formula that incorporates total surface area, lateral surface area, side lengths, and angles between them. This formula provides an accurate measurement of the three-dimensional space enclosed by the parallelepiped.

2. How Does The Calculator Work?

The calculator uses the volume formula:

Where:

\( V \) — Volume of Parallelepiped (m³)
\( TSA \) — Total Surface Area of Parallelepiped (m²)
\( LSA \) — Lateral Surface Area of Parallelepiped (m²)
\( \beta \) — Angle Beta of Parallelepiped (degrees)
\( S_b \) — Side B of Parallelepiped (m)
\( \alpha \) — Angle Alpha of Parallelepiped (degrees)
\( \gamma \) — Angle Gamma of Parallelepiped (degrees)

Explanation: The formula accounts for the geometric relationships between surface areas, side lengths, and angles to calculate the volume of the parallelepiped.

3. Importance Of Volume Calculation

Details: Accurate volume calculation is crucial for determining the capacity of three-dimensional objects, structural analysis, and various engineering applications involving parallelepiped shapes.

4. Using The Calculator

Tips: Enter all required values in appropriate units. Total and lateral surface areas must be positive values, angles must be between 0-180 degrees, and side lengths must be positive.

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: How is this formula derived?
A: The formula is derived from geometric principles relating surface areas to volume through trigonometric relationships of the angles between sides.

Q3: What are the units for volume measurement?
A: Volume is measured in cubic units (m³, cm³, etc.) depending on the units used for side measurements.

Q4: Can this calculator handle different units?
A: The calculator uses consistent units (meters for length, square meters for area). Convert all measurements to consistent units before calculation.

Q5: What if I get a negative value under the square root?
A: This indicates invalid input values that don't form a valid parallelepiped. Check your measurements and angles.