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Volume of Regular Icosahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
volume = (5*(3+sqrt(5))*Side^3)/12
V = (5*(3+sqrt(5))*s^3)/12
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Side - The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Side: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = (5*(3+sqrt(5))*s^3)/12 --> (5*(3+sqrt(5))*9^3)/12
Evaluating ... ...
V = 1590.45564816556
STEP 3: Convert Result to Output's Unit
1590.45564816556 Cubic Meter --> No Conversion Required
FINAL ANSWER
1590.45564816556 Cubic Meter <-- Volume
(Calculation completed in 00.016 seconds)

10+ Volume Calculators

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volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go
Volume of a Capsule
volume = pi*((Radius)^2)*((4/3)*Radius+Height) Go
Volume of hollow cylinder
volume = pi*Height*(Radius 2^2-Radius 1^2) Go
Volume of a Circular Cone
volume = (1/3)*pi*(Radius)^2*Height Go
Volume of a Circular Cylinder
volume = pi*(Radius)^2*Height Go
Volume of a Rectangular Prism
volume = Width*Height*Length Go
Volume of a Hemisphere
volume = (2/3)*pi*(Radius)^3 Go
Volume of a Sphere
volume = (4/3)*pi*(Radius)^3 Go
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Volume of a Cube
volume = Side^3 Go

6 Volume of Platonic Solids Calculators

Volume of Platonic Solids
volume_platonic = (1/24)*Length of edge^3*Number of edges in a face*Number of faces* cos((180*pi/180)/Number of edges meeting at a vertex)/(sin((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*cos((0.5*pi/180)*Dihedral Angle)) Go
Volume of Regular Dodecahedron
volume = ((15+(7*sqrt(5)))*Side^3)/4 Go
Volume of Regular Icosahedron
volume = (5*(3+sqrt(5))*Side^3)/12 Go
Volume of Regular Tetrahedron
volume = (Side^3)/(6*sqrt(2)) Go
Volume of Regular Octahedron
volume = (sqrt(2))*(Side^3)/3 Go
Volume of a Cube
volume = Side^3 Go

Volume of Regular Icosahedron Formula

volume = (5*(3+sqrt(5))*Side^3)/12
V = (5*(3+sqrt(5))*s^3)/12

How many edges does a icosahedron have?

There are two objects, one convex and one nonconvex, that can both be called regular icosahedra. Each has 30 edges and 20 equilateral triangle faces with five meeting at each of its twelve vertices. The icosahedron is the dual of the dodecahedron having three regular pentagonal faces around each vertex. The icosahedron represents the WATER element, symbolizing dreams, intuition, and emotions.

How to Calculate Volume of Regular Icosahedron?

Volume of Regular Icosahedron calculator uses volume = (5*(3+sqrt(5))*Side^3)/12 to calculate the Volume, Volume of Regular Icosahedron, is the amount of the space which the shapes takes up. Volume and is denoted by V symbol.

How to calculate Volume of Regular Icosahedron using this online calculator? To use this online calculator for Volume of Regular Icosahedron, enter Side (s) and hit the calculate button. Here is how the Volume of Regular Icosahedron calculation can be explained with given input values -> 1590.456 = (5*(3+sqrt(5))*9^3)/12.

FAQ

What is Volume of Regular Icosahedron?
Volume of Regular Icosahedron, is the amount of the space which the shapes takes up and is represented as V = (5*(3+sqrt(5))*s^3)/12 or volume = (5*(3+sqrt(5))*Side^3)/12. The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back.
How to calculate Volume of Regular Icosahedron?
Volume of Regular Icosahedron, is the amount of the space which the shapes takes up is calculated using volume = (5*(3+sqrt(5))*Side^3)/12. To calculate Volume of Regular Icosahedron, you need Side (s). With our tool, you need to enter the respective value for Side 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?
In this formula, Volume uses Side. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • volume_platonic = (1/24)*Length of edge^3*Number of edges in a face*Number of faces* cos((180*pi/180)/Number of edges meeting at a vertex)/(sin((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*tan((180*pi/180)/Number of edges in a face)*cos((0.5*pi/180)*Dihedral Angle))
  • volume = Side^3
  • volume = ((15+(7*sqrt(5)))*Side^3)/4
  • volume = (5*(3+sqrt(5))*Side^3)/12
  • volume = (sqrt(2))*(Side^3)/3
  • volume = (Side^3)/(6*sqrt(2))
Where is the Volume of Regular Icosahedron calculator used?
Among many, Volume of Regular Icosahedron calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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