Insphere Radius of Disphenoid Calculator

Formula Used:

\[ r_i = \frac{3}{4} \times \frac{\sqrt{\frac{(S_a^2 + S_b^2 - S_c^2) \times (S_a^2 - S_b^2 + S_c^2) \times (-S_a^2 + S_b^2 + S_c^2)}{72}}}{\sqrt{\frac{P}{8} \times (\frac{P}{8} - S_a) \times (\frac{P}{8} - S_b) \times (\frac{P}{8} - S_c)}} \]

Side A of Disphenoid:

Side B of Disphenoid:

Side C of Disphenoid:

Perimeter of Disphenoid:

Insphere Radius of Disphenoid:

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1. What is Insphere Radius of Disphenoid?

The Insphere Radius of a Disphenoid is the radius of the sphere that is contained by the Disphenoid in such a way that all the faces just touch the sphere. A Disphenoid is a tetrahedron whose four faces are congruent acute-angled triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( r_i \) — Insphere Radius of Disphenoid (m)
\( S_a \) — Side A of Disphenoid (m)
\( S_b \) — Side B of Disphenoid (m)
\( S_c \) — Side C of Disphenoid (m)
\( P \) — Perimeter of Disphenoid (m)

Explanation: The formula calculates the radius of the inscribed sphere based on the side lengths and perimeter of the disphenoid.

3. Importance of Insphere Radius Calculation

Details: Calculating the insphere radius is important in geometry and 3D modeling for understanding the spatial properties of disphenoids and their inscribed spheres.

4. Using the Calculator

Tips: Enter all side lengths and the perimeter in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a Disphenoid?
A: A Disphenoid is a tetrahedron with four congruent acute-angled triangular faces.

Q2: Why is the insphere radius important?
A: The insphere radius helps understand the spatial relationships and geometric properties of the disphenoid.

Q3: What units should I use?
A: All measurements should be in consistent units (typically meters).

Q4: Are there any limitations to this formula?
A: The formula assumes a valid disphenoid with positive side lengths that satisfy triangle inequalities.

Q5: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.