Volume of Icosahedron given Insphere Radius Calculator

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

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

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Volume of Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3
V = 5/12*(3+sqrt(5))*((12*r_i)/(sqrt(3)*(3+sqrt(5))))^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 Icosahedron - (Measured in Cubic Meter) - Volume of Icosahedron is the total quantity of three dimensional space enclosed by the surface of the Icosahedron.
Insphere Radius of Icosahedron - (Measured in Meter) - Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Icosahedron: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5/12*(3+sqrt(5))*((12*r_i)/(sqrt(3)*(3+sqrt(5))))^3 --> 5/12*(3+sqrt(5))*((12*7)/(sqrt(3)*(3+sqrt(5))))^3

Evaluating ... ...

V = 1733.54125725442

STEP 3: Convert Result to Output's Unit

1733.54125725442 Cubic Meter --> No Conversion Required

FINAL ANSWER

1733.54125725442 ≈ 1733.541 Cubic Meter <-- Volume of Icosahedron

(Calculation completed in 00.020 seconds)

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

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< Volume of Icosahedron Calculators

Volume of Icosahedron given Circumsphere Radius

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3

Volume of Icosahedron given Insphere Radius

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3

Volume of Icosahedron given Total Surface Area

LaTeX Go Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)

Volume of Icosahedron

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3

< Volume of Icosahedron Calculators

Volume of Icosahedron given Circumsphere Radius

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3

Volume of Icosahedron given Insphere Radius

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3

Volume of Icosahedron given Total Surface Area

LaTeX Go Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)

Volume of Icosahedron

LaTeX Go Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3

Volume of Icosahedron given Insphere Radius Formula

LaTeX Go

Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3
V = 5/12*(3+sqrt(5))*((12*r_i)/(sqrt(3)*(3+sqrt(5))))^3

What is an Icosahedron?

An Icosahedron is a symmetric and closed three dimensional shape with 20 identical equilateral triangular faces. It is a Platonic solid, which has 20 faces, 12 vertices and 30 edges. At each vertex, five equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Volume of Icosahedron given Insphere Radius?

Volume of Icosahedron given Insphere Radius calculator uses Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3 to calculate the Volume of Icosahedron, The Volume of Icosahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the insphere radius of the Icosahedron. Volume of Icosahedron is denoted by V symbol.

How to calculate Volume of Icosahedron given Insphere Radius using this online calculator? To use this online calculator for Volume of Icosahedron given Insphere Radius, enter Insphere Radius of Icosahedron (r_i) and hit the calculate button. Here is how the Volume of Icosahedron given Insphere Radius calculation can be explained with given input values -> 1733.541 = 5/12*(3+sqrt(5))*((12*7)/(sqrt(3)*(3+sqrt(5))))^3.

FAQ

What is Volume of Icosahedron given Insphere Radius?

The Volume of Icosahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the insphere radius of the Icosahedron and is represented as V = 5/12*(3+sqrt(5))*((12*r_i)/(sqrt(3)*(3+sqrt(5))))^3 or Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3. Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.

How to calculate Volume of Icosahedron given Insphere Radius?

The Volume of Icosahedron given Insphere Radius formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the insphere radius of the Icosahedron is calculated using Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3. To calculate Volume of Icosahedron given Insphere Radius, you need Insphere Radius of Icosahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of 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 Icosahedron?

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

Volume of Icosahedron = (3+sqrt(5))/(12*sqrt(5))*(Total Surface Area of Icosahedron/sqrt(3))^(3/2)
Volume of Icosahedron = 5/12*(3+sqrt(5))*Edge Length of Icosahedron^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3

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