Volume of Triakis Icosahedron given Insphere Radius Calculator

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

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✖Volume of Triakis Icosahedron is the quantity of three dimensional space enclosed by the entire surface of Triakis Icosahedron.ⓘ Volume of Triakis Icosahedron given Insphere Radius [V]

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Volume of Triakis Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^3)
V = (5/44)*(5+(7*sqrt(5)))*(((4*r_i)/(sqrt((10*(33+(13*sqrt(5))))/61)))^3)
This formula uses 1 Functions, 2 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

Volume of Triakis Icosahedron - (Measured in Cubic Meter) - Volume of Triakis Icosahedron is the quantity of three dimensional space enclosed by the entire surface of Triakis Icosahedron.
Insphere Radius of Triakis Icosahedron - (Measured in Meter) - Insphere Radius of Triakis Icosahedron is the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Triakis Icosahedron: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (5/44)*(5+(7*sqrt(5)))*(((4*r_i)/(sqrt((10*(33+(13*sqrt(5))))/61)))^3) --> (5/44)*(5+(7*sqrt(5)))*(((4*6)/(sqrt((10*(33+(13*sqrt(5))))/61)))^3)

Evaluating ... ...

V = 999.555760014357

STEP 3: Convert Result to Output's Unit

999.555760014357 Cubic Meter --> No Conversion Required

FINAL ANSWER

999.555760014357 ≈ 999.5558 Cubic Meter <-- Volume of Triakis Icosahedron

(Calculation completed in 00.020 seconds)

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< Volume of Triakis Icosahedron Calculators

Volume of Triakis Icosahedron given Total Surface Area

LaTeX Go Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*(((11*Total Surface Area of Triakis Icosahedron)/(15*sqrt(109-(30*sqrt(5)))))^(3/2))

Volume of Triakis Icosahedron given Pyramidal Edge Length

LaTeX Go Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*(((22*Pyramidal Edge Length of Triakis Icosahedron)/(15-sqrt(5)))^3)

Volume of Triakis Icosahedron given Midsphere Radius

LaTeX Go Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*(((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))^3)

Volume of Triakis Icosahedron

LaTeX Go Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*((Icosahedral Edge Length of Triakis Icosahedron)^3)

Volume of Triakis Icosahedron given Insphere Radius Formula

LaTeX Go

What is Triakis Icosahedron?

The Triakis Icosahedron is a three-dimensional polyhedron created from the dual of the truncated dodecahedron. Because of this, it shares the same full icosahedral symmetry group as the dodecahedron and the truncated dodecahedron. It can also be constructed by adding short triangular pyramids onto the faces of an icosahedron. It has 60 faces, 90 edges, 32 vertices.

How to Calculate Volume of Triakis Icosahedron given Insphere Radius?

Volume of Triakis Icosahedron given Insphere Radius calculator uses Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^3) to calculate the Volume of Triakis Icosahedron, Volume of Triakis Icosahedron given Insphere Radius formula is defined as quantity of three dimensional space covered by closed surface of Triakis Icosahedron, calculated using insphere radius of Triakis Icosahedron. Volume of Triakis Icosahedron is denoted by V symbol.

How to calculate Volume of Triakis Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Volume of Triakis Icosahedron given Insphere Radius, enter Insphere Radius of Triakis Icosahedron (r_i) and hit the calculate button. Here is how the Volume of Triakis Icosahedron given Insphere Radius calculation can be explained with given input values -> 999.5558 = (5/44)*(5+(7*sqrt(5)))*(((4*6)/(sqrt((10*(33+(13*sqrt(5))))/61)))^3).

FAQ

What is Volume of Triakis Icosahedron given Insphere Radius?

Volume of Triakis Icosahedron given Insphere Radius formula is defined as quantity of three dimensional space covered by closed surface of Triakis Icosahedron, calculated using insphere radius of Triakis Icosahedron and is represented as V = (5/44)*(5+(7*sqrt(5)))*(((4*r_i)/(sqrt((10*(33+(13*sqrt(5))))/61)))^3) or Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^3). Insphere Radius of Triakis Icosahedron is the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere.

How to calculate Volume of Triakis Icosahedron given Insphere Radius?

Volume of Triakis Icosahedron given Insphere Radius formula is defined as quantity of three dimensional space covered by closed surface of Triakis Icosahedron, calculated using insphere radius of Triakis Icosahedron is calculated using Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*(((4*Insphere Radius of Triakis Icosahedron)/(sqrt((10*(33+(13*sqrt(5))))/61)))^3). To calculate Volume of Triakis Icosahedron given Insphere Radius, you need Insphere Radius of Triakis Icosahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Triakis Icosahedron 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 Volume of Triakis Icosahedron?

In this formula, Volume of Triakis Icosahedron uses Insphere Radius of Triakis Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*((Icosahedral Edge Length of Triakis Icosahedron)^3)
Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*(((22*Pyramidal Edge Length of Triakis Icosahedron)/(15-sqrt(5)))^3)
Volume of Triakis Icosahedron = (5/44)*(5+(7*sqrt(5)))*(((11*Total Surface Area of Triakis Icosahedron)/(15*sqrt(109-(30*sqrt(5)))))^(3/2))

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