Volume of Icosahedron given Surface to Volume Ratio Calculator

✖The Surface to Volume Ratio of Icosahedron is the numerical ratio of the total surface area to the volume of the Icosahedron.ⓘ Surface to Volume Ratio of Icosahedron [R_A/V]

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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 Surface to Volume Ratio [V]

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Formula

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Volume of Icosahedron given Surface to Volume Ratio

Formula

`"V" = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*"R"_{"A/V"}))^3`

Example

`"2132.18m³"=5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*"0.4m⁻¹"))^3`

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Volume of Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^3
V = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*R_A/V))^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.
Surface to Volume Ratio of Icosahedron - (Measured in 1 per Meter) - The Surface to Volume Ratio of Icosahedron is the numerical ratio of the total surface area to the volume of the Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Icosahedron: 0.4 1 per Meter --> 0.4 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*R_A/V))^3 --> 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*0.4))^3

Evaluating ... ...

V = 2132.17993558079

STEP 3: Convert Result to Output's Unit

2132.17993558079 Cubic Meter --> No Conversion Required

FINAL ANSWER

2132.17993558079 ≈ 2132.18 Cubic Meter <-- Volume of Icosahedron

(Calculation completed in 00.020 seconds)

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Created by Dhruv Walia

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

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< 11 Volume of Icosahedron Calculators

Volume of Icosahedron given Surface to Volume Ratio

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^3

Volume of Icosahedron given Circumsphere Radius

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

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

Volume of Icosahedron given Space Diagonal

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3

Volume of Icosahedron given Total Surface Area

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

Volume of Icosahedron given Lateral Surface Area

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))^(3/2)

Volume of Icosahedron given Midsphere Radius

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^3

Volume of Icosahedron given Face Area

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Face Area of Icosahedron)/sqrt(3))^(3/2)

Volume of Icosahedron given Face Perimeter

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*(Face Perimeter of Icosahedron/3)^3

Volume of Icosahedron given Perimeter

Go Volume of Icosahedron = 5/12*(3+sqrt(5))*(Perimeter of Icosahedron/30)^3

Volume of Icosahedron

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

Volume of Icosahedron given Surface to Volume Ratio Formula

Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^3
V = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*R_A/V))^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 Surface to Volume Ratio?

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

How to calculate Volume of Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Volume of Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Icosahedron (R_A/V) and hit the calculate button. Here is how the Volume of Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 2132.18 = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*0.4))^3.

FAQ

What is Volume of Icosahedron given Surface to Volume Ratio?

The Volume of Icosahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the surface to volume ratio of the Icosahedron and is represented as V = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*R_A/V))^3 or Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^3. The Surface to Volume Ratio of Icosahedron is the numerical ratio of the total surface area to the volume of the Icosahedron.

How to calculate Volume of Icosahedron given Surface to Volume Ratio?

The Volume of Icosahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the surface to volume ratio of the Icosahedron is calculated using Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron))^3. To calculate Volume of Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Icosahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio of Icosahedron. We can use 10 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
Volume of Icosahedron = 5/12*(3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*(Face Perimeter of Icosahedron/3)^3
Volume of Icosahedron = 5/12*(3+sqrt(5))*((4*Face Area of Icosahedron)/sqrt(3))^(3/2)
Volume of Icosahedron = 5/12*(3+sqrt(5))*((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))^(3/2)
Volume of Icosahedron = 5/12*(3+sqrt(5))*(Perimeter of Icosahedron/30)^3

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