Insphere Radius of Disphenoid Calculator

✖Side A of Disphenoid is the length of the first edge of any of the congruent triangular faces of the Disphenoid.ⓘ Side A of Disphenoid [S_a]			+10% -10%
✖Side B of Disphenoid is the length of the second edge of any of the congruent triangular faces of the Disphenoid.ⓘ Side B of Disphenoid [S_b]			+10% -10%
✖Side C of Disphenoid is the length of the third edge of any of the congruent triangular faces of the Disphenoid.ⓘ Side C of Disphenoid [S_c]			+10% -10%
✖Perimeter of Disphenoid is the total distance around the edge of the Disphenoid.ⓘ Perimeter of Disphenoid [P]			+10% -10%

✖Insphere Radius of Disphenoid is the radius of the sphere that is contained by the Disphenoid in such a way that all the faces just touching the sphere.ⓘ Insphere Radius of Disphenoid [r_i]

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Insphere Radius of Disphenoid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Disphenoid = 3/4*sqrt(((Side A of Disphenoid^2+Side B of Disphenoid^2-Side C of Disphenoid^2)*(Side A of Disphenoid^2-Side B of Disphenoid^2+Side C of Disphenoid^2)*(-Side A of Disphenoid^2+Side B of Disphenoid^2+Side C of Disphenoid^2))/72)/sqrt(Perimeter of Disphenoid/8*(Perimeter of Disphenoid/8-Side A of Disphenoid)*(Perimeter of Disphenoid/8-Side B of Disphenoid)*(Perimeter of Disphenoid/8-Side C of Disphenoid))
r_i = 3/4*sqrt(((S_a^2+S_b^2-S_c^2)*(S_a^2-S_b^2+S_c^2)*(-S_a^2+S_b^2+S_c^2))/72)/sqrt(P/8*(P/8-S_a)*(P/8-S_b)*(P/8-S_c))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Insphere Radius of Disphenoid - (Measured in Meter) - Insphere Radius of Disphenoid is the radius of the sphere that is contained by the Disphenoid in such a way that all the faces just touching the sphere.
Side A of Disphenoid - (Measured in Meter) - Side A of Disphenoid is the length of the first edge of any of the congruent triangular faces of the Disphenoid.
Side B of Disphenoid - (Measured in Meter) - Side B of Disphenoid is the length of the second edge of any of the congruent triangular faces of the Disphenoid.
Side C of Disphenoid - (Measured in Meter) - Side C of Disphenoid is the length of the third edge of any of the congruent triangular faces of the Disphenoid.
Perimeter of Disphenoid - (Measured in Meter) - Perimeter of Disphenoid is the total distance around the edge of the Disphenoid.

STEP 1: Convert Input(s) to Base Unit

Side A of Disphenoid: 10 Meter --> 10 Meter No Conversion Required
Side B of Disphenoid: 13 Meter --> 13 Meter No Conversion Required
Side C of Disphenoid: 15 Meter --> 15 Meter No Conversion Required
Perimeter of Disphenoid: 152 Meter --> 152 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = 3/4*sqrt(((S_a^2+S_b^2-S_c^2)*(S_a^2-S_b^2+S_c^2)*(-S_a^2+S_b^2+S_c^2))/72)/sqrt(P/8*(P/8-S_a)*(P/8-S_b)*(P/8-S_c)) --> 3/4*sqrt(((10^2+13^2-15^2)*(10^2-13^2+15^2)*(-10^2+13^2+15^2))/72)/sqrt(152/8*(152/8-10)*(152/8-13)*(152/8-15))

Evaluating ... ...

r_i = 2.54064186990436

STEP 3: Convert Result to Output's Unit

2.54064186990436 Meter --> No Conversion Required

FINAL ANSWER

2.54064186990436 ≈ 2.540642 Meter <-- Insphere Radius of Disphenoid

(Calculation completed in 00.004 seconds)

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Created by Nikhil

Mumbai University (DJSCE), Mumbai

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Insphere Radius of Disphenoid Calculators

Insphere Radius of Disphenoid

LaTeX Go Insphere Radius of Disphenoid = 3/4*sqrt(((Side A of Disphenoid^2+Side B of Disphenoid^2-Side C of Disphenoid^2)*(Side A of Disphenoid^2-Side B of Disphenoid^2+Side C of Disphenoid^2)*(-Side A of Disphenoid^2+Side B of Disphenoid^2+Side C of Disphenoid^2))/72)/sqrt(Perimeter of Disphenoid/8*(Perimeter of Disphenoid/8-Side A of Disphenoid)*(Perimeter of Disphenoid/8-Side B of Disphenoid)*(Perimeter of Disphenoid/8-Side C of Disphenoid))

Insphere Radius of Disphenoid given Volume and Total Surface Area

LaTeX Go Insphere Radius of Disphenoid = (3*Volume of Disphenoid)/Total Surface Area of Disphenoid

Insphere Radius of Disphenoid Formula

LaTeX Go

What is a Disphenoid?

In geometry, a Disphenoid (from Greek sphenoeides, "wedgelike") is a tetrahedron whose four faces are congruent acute-angled triangles. It can also be described as a tetrahedron in which every two edges that are opposite each other have equal lengths. Other names for the same shape are sphenoid, bisphenoid, isosceles tetrahedron, equifacial tetrahedron, almost regular tetrahedron, and tetramonohedron. All the solid angles and vertex figures of a Disphenoid are the same, and the sum of the face angles at each vertex is equal to two right angles. However, a Disphenoid is not a regular polyhedron, because, in general, its faces are not regular polygons, and its edges have three different lengths.

How to Calculate Insphere Radius of Disphenoid?

Insphere Radius of Disphenoid calculator uses Insphere Radius of Disphenoid = 3/4*sqrt(((Side A of Disphenoid^2+Side B of Disphenoid^2-Side C of Disphenoid^2)*(Side A of Disphenoid^2-Side B of Disphenoid^2+Side C of Disphenoid^2)*(-Side A of Disphenoid^2+Side B of Disphenoid^2+Side C of Disphenoid^2))/72)/sqrt(Perimeter of Disphenoid/8*(Perimeter of Disphenoid/8-Side A of Disphenoid)*(Perimeter of Disphenoid/8-Side B of Disphenoid)*(Perimeter of Disphenoid/8-Side C of Disphenoid)) to calculate the Insphere Radius of Disphenoid, The Insphere Radius of Disphenoid formula is defined as the radius of the sphere that is contained by the Disphenoid in such a way that all the faces just touching the sphere. Insphere Radius of Disphenoid is denoted by r_i symbol.

How to calculate Insphere Radius of Disphenoid using this online calculator? To use this online calculator for Insphere Radius of Disphenoid, enter Side A of Disphenoid (S_a), Side B of Disphenoid (S_b), Side C of Disphenoid (S_c) & Perimeter of Disphenoid (P) and hit the calculate button. Here is how the Insphere Radius of Disphenoid calculation can be explained with given input values -> 2.540642 = 3/4*sqrt(((10^2+13^2-15^2)*(10^2-13^2+15^2)*(-10^2+13^2+15^2))/72)/sqrt(152/8*(152/8-10)*(152/8-13)*(152/8-15)).

FAQ

What is Insphere Radius of Disphenoid?

The Insphere Radius of Disphenoid formula is defined as the radius of the sphere that is contained by the Disphenoid in such a way that all the faces just touching the sphere and is represented as r_i = 3/4*sqrt(((S_a^2+S_b^2-S_c^2)*(S_a^2-S_b^2+S_c^2)*(-S_a^2+S_b^2+S_c^2))/72)/sqrt(P/8*(P/8-S_a)*(P/8-S_b)*(P/8-S_c)) or Insphere Radius of Disphenoid = 3/4*sqrt(((Side A of Disphenoid^2+Side B of Disphenoid^2-Side C of Disphenoid^2)*(Side A of Disphenoid^2-Side B of Disphenoid^2+Side C of Disphenoid^2)*(-Side A of Disphenoid^2+Side B of Disphenoid^2+Side C of Disphenoid^2))/72)/sqrt(Perimeter of Disphenoid/8*(Perimeter of Disphenoid/8-Side A of Disphenoid)*(Perimeter of Disphenoid/8-Side B of Disphenoid)*(Perimeter of Disphenoid/8-Side C of Disphenoid)). Side A of Disphenoid is the length of the first edge of any of the congruent triangular faces of the Disphenoid, Side B of Disphenoid is the length of the second edge of any of the congruent triangular faces of the Disphenoid, Side C of Disphenoid is the length of the third edge of any of the congruent triangular faces of the Disphenoid & Perimeter of Disphenoid is the total distance around the edge of the Disphenoid.

How to calculate Insphere Radius of Disphenoid?

The Insphere Radius of Disphenoid formula is defined as the radius of the sphere that is contained by the Disphenoid in such a way that all the faces just touching the sphere is calculated using Insphere Radius of Disphenoid = 3/4*sqrt(((Side A of Disphenoid^2+Side B of Disphenoid^2-Side C of Disphenoid^2)*(Side A of Disphenoid^2-Side B of Disphenoid^2+Side C of Disphenoid^2)*(-Side A of Disphenoid^2+Side B of Disphenoid^2+Side C of Disphenoid^2))/72)/sqrt(Perimeter of Disphenoid/8*(Perimeter of Disphenoid/8-Side A of Disphenoid)*(Perimeter of Disphenoid/8-Side B of Disphenoid)*(Perimeter of Disphenoid/8-Side C of Disphenoid)). To calculate Insphere Radius of Disphenoid, you need Side A of Disphenoid (S_a), Side B of Disphenoid (S_b), Side C of Disphenoid (S_c) & Perimeter of Disphenoid (P). With our tool, you need to enter the respective value for Side A of Disphenoid, Side B of Disphenoid, Side C of Disphenoid & Perimeter of Disphenoid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Insphere Radius of Disphenoid?

In this formula, Insphere Radius of Disphenoid uses Side A of Disphenoid, Side B of Disphenoid, Side C of Disphenoid & Perimeter of Disphenoid. We can use 1 other way(s) to calculate the same, which is/are as follows -

Insphere Radius of Disphenoid = (3*Volume of Disphenoid)/Total Surface Area of Disphenoid

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