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Volume (V) of Great Dodecahedron given Pyramid height (hp) Solution

STEP 0: Pre-Calculation Summary
Formula Used
volume = ((5/4)*(sqrt(5)-1))*(((6*Height)/(sqrt(3)*(3-sqrt(5))))^3)
V = ((5/4)*(sqrt(5)-1))*(((6*h)/(sqrt(3)*(3-sqrt(5))))^3)
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Height - Height is the distance between the lowest and highest points of a person standing upright. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Height: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = ((5/4)*(sqrt(5)-1))*(((6*h)/(sqrt(3)*(3-sqrt(5))))^3) --> ((5/4)*(sqrt(5)-1))*(((6*12)/(sqrt(3)*(3-sqrt(5))))^3)
Evaluating ... ...
V = 248945.24198063
STEP 3: Convert Result to Output's Unit
248945.24198063 Cubic Meter --> No Conversion Required
FINAL ANSWER
248945.24198063 Cubic Meter <-- Volume
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

Volume of a Conical Frustum
volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go
Total Surface Area of a Cone
total_surface_area = pi*Radius*(Radius+sqrt(Radius^2+Height^2)) Go
Lateral Surface Area of a Cone
lateral_surface_area = pi*Radius*sqrt(Radius^2+Height^2) Go
Total Surface Area of a Cylinder
total_surface_area = 2*pi*Radius*(Height+Radius) Go
Lateral Surface Area of a Cylinder
lateral_surface_area = 2*pi*Radius*Height Go
Volume of a Circular Cone
volume = (1/3)*pi*(Radius)^2*Height Go
Area of a Trapezoid
area = ((Base A+Base B)/2)*Height Go
Volume of a Circular Cylinder
volume = pi*(Radius)^2*Height Go
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Area of a Triangle when base and height are given
area = 1/2*Base*Height Go
Area of a Parallelogram when base and height are given
area = Base*Height 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 Pyramid height (hp) Formula

volume = ((5/4)*(sqrt(5)-1))*(((6*Height)/(sqrt(3)*(3-sqrt(5))))^3)
V = ((5/4)*(sqrt(5)-1))*(((6*h)/(sqrt(3)*(3-sqrt(5))))^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 Pyramid height (hp)?

Volume (V) of Great Dodecahedron given Pyramid height (hp) calculator uses volume = ((5/4)*(sqrt(5)-1))*(((6*Height)/(sqrt(3)*(3-sqrt(5))))^3) to calculate the Volume, The Volume (V) of Great Dodecahedron given Pyramid height (hp) 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 Pyramid height (hp) using this online calculator? To use this online calculator for Volume (V) of Great Dodecahedron given Pyramid height (hp), enter Height (h) and hit the calculate button. Here is how the Volume (V) of Great Dodecahedron given Pyramid height (hp) calculation can be explained with given input values -> 248945.2 = ((5/4)*(sqrt(5)-1))*(((6*12)/(sqrt(3)*(3-sqrt(5))))^3).

FAQ

What is Volume (V) of Great Dodecahedron given Pyramid height (hp)?
The Volume (V) of Great Dodecahedron given Pyramid height (hp) formula is defined as amount of three dimensional space covered by Great Dodecahedron and is represented as V = ((5/4)*(sqrt(5)-1))*(((6*h)/(sqrt(3)*(3-sqrt(5))))^3) or volume = ((5/4)*(sqrt(5)-1))*(((6*Height)/(sqrt(3)*(3-sqrt(5))))^3). Height is the distance between the lowest and highest points of a person standing upright.
How to calculate Volume (V) of Great Dodecahedron given Pyramid height (hp)?
The Volume (V) of Great Dodecahedron given Pyramid height (hp) formula is defined as amount of three dimensional space covered by Great Dodecahedron is calculated using volume = ((5/4)*(sqrt(5)-1))*(((6*Height)/(sqrt(3)*(3-sqrt(5))))^3). To calculate Volume (V) of Great Dodecahedron given Pyramid height (hp), you need Height (h). With our tool, you need to enter the respective value for Height 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 Height. 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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