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Volume (V) of Great Dodecahedron given Edge length (a) Solution

STEP 0: Pre-Calculation Summary
Formula Used
volume = ((5/4)*(sqrt(5)-1))*(Side^3)
V = ((5/4)*(sqrt(5)-1))*(s^3)
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 = ((5/4)*(sqrt(5)-1))*(s^3) --> ((5/4)*(sqrt(5)-1))*(9^3)
Evaluating ... ...
V = 1126.36694449668
STEP 3: Convert Result to Output's Unit
1126.36694449668 Cubic Meter --> No Conversion Required
FINAL ANSWER
1126.36694449668 Cubic Meter <-- Volume
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

Total Surface Area of a Pyramid
total_surface_area = Side*(Side+sqrt(Side^2+4*(Height)^2)) Go
Area of a Rhombus when side and diagonals are given
area = (1/2)*(Diagonal A)*(sqrt(4*Side^2-(Diagonal A)^2)) Go
Lateral Surface Area of a Pyramid
lateral_surface_area = Side*sqrt(Side^2+4*(Height)^2) Go
Surface Area of a Capsule
surface_area = 2*pi*Radius*(2*Radius+Side) Go
Volume of a Capsule
volume = pi*(Radius)^2*((4/3)*Radius+Side) Go
Area of a Octagon
area = 2*(1+sqrt(2))*(Side)^2 Go
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Area of a Hexagon
area = (3/2)*sqrt(3)*Side^2 Go
Base Surface Area of a Pyramid
base_surface_area = Side^2 Go
Surface Area of a Cube
surface_area = 6*Side^2 Go
Volume of a Cube
volume = Side^3 Go

11 Other formulas that calculate the same Output

Volume of a Conical Frustum
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+Side) 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 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 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

Volume (V) of Great Dodecahedron given Edge length (a) Formula

volume = ((5/4)*(sqrt(5)-1))*(Side^3)
V = ((5/4)*(sqrt(5)-1))*(s^3)

What is Great Dodecahedron?

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5,5/2} and Coxeter–Dynkin diagram of. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Volume (V) of Great Dodecahedron given Edge length (a)?

Volume (V) of Great Dodecahedron given Edge length (a) calculator uses volume = ((5/4)*(sqrt(5)-1))*(Side^3) to calculate the Volume, The Volume (V) of Great Dodecahedron given Edge length (a) formula is defined as amount of three dimensional space covered by Great Dodecahedron. Volume and is denoted by V symbol.

How to calculate Volume (V) of Great Dodecahedron given Edge length (a) using this online calculator? To use this online calculator for Volume (V) of Great Dodecahedron given Edge length (a), enter Side (s) and hit the calculate button. Here is how the Volume (V) of Great Dodecahedron given Edge length (a) calculation can be explained with given input values -> 1126.367 = ((5/4)*(sqrt(5)-1))*(9^3).

FAQ

What is Volume (V) of Great Dodecahedron given Edge length (a)?
The Volume (V) of Great Dodecahedron given Edge length (a) formula is defined as amount of three dimensional space covered by Great Dodecahedron and is represented as V = ((5/4)*(sqrt(5)-1))*(s^3) or volume = ((5/4)*(sqrt(5)-1))*(Side^3). 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 (V) of Great Dodecahedron given Edge length (a)?
The Volume (V) of Great Dodecahedron given Edge length (a) formula is defined as amount of three dimensional space covered by Great Dodecahedron is calculated using volume = ((5/4)*(sqrt(5)-1))*(Side^3). To calculate Volume (V) of Great Dodecahedron given Edge length (a), 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 11 other way(s) to calculate the same, which is/are as follows -
  • volume = pi*(Radius)^2*((4/3)*Radius+Side)
  • volume = (1/3)*pi*(Radius)^2*Height
  • volume = pi*(Radius)^2*Height
  • volume = Side^3
  • volume = (2/3)*pi*(Radius)^3
  • volume = (4/3)*pi*(Radius)^3
  • volume = (1/3)*Side^2*Height
  • volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2))
  • volume = Width*Height*Length
  • volume = ((15+(7*sqrt(5)))*Side^3)/4
  • volume = (5*(3+sqrt(5))*Side^3)/12
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