Volume of Icosahedron given Face Perimeter Calculator

✖Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.ⓘ Face Perimeter of Icosahedron [P_Face]

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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 Face Perimeter [V]

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Volume of Icosahedron given Face Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Icosahedron = 5/12*(3+sqrt(5))*(Face Perimeter of Icosahedron/3)^3
V = 5/12*(3+sqrt(5))*(P_Face/3)^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.
Face Perimeter of Icosahedron - (Measured in Meter) - Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.

STEP 1: Convert Input(s) to Base Unit

Face Perimeter of Icosahedron: 30 Meter --> 30 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5/12*(3+sqrt(5))*(P_Face/3)^3 --> 5/12*(3+sqrt(5))*(30/3)^3

Evaluating ... ...

V = 2181.69499062491

STEP 3: Convert Result to Output's Unit

2181.69499062491 Cubic Meter --> No Conversion Required

FINAL ANSWER

2181.69499062491 ≈ 2181.695 Cubic Meter <-- Volume of Icosahedron

(Calculation completed in 00.004 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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< 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 Face Perimeter Formula

LaTeX Go

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

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

How to calculate Volume of Icosahedron given Face Perimeter using this online calculator? To use this online calculator for Volume of Icosahedron given Face Perimeter, enter Face Perimeter of Icosahedron (P_Face) and hit the calculate button. Here is how the Volume of Icosahedron given Face Perimeter calculation can be explained with given input values -> 2181.695 = 5/12*(3+sqrt(5))*(30/3)^3.

FAQ

What is Volume of Icosahedron given Face Perimeter?

The Volume of Icosahedron given Face Perimeter formula is defined as the total quantity of three dimensional space enclosed by the surface of the Icosahedron, and calculated using the face perimeter of the Icosahedron and is represented as V = 5/12*(3+sqrt(5))*(P_Face/3)^3 or Volume of Icosahedron = 5/12*(3+sqrt(5))*(Face Perimeter of Icosahedron/3)^3. Face Perimeter of Icosahedron is the total distance around the five edges of any face of the Icosahedron.

How to calculate Volume of Icosahedron given Face Perimeter?

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