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Edge length of Great Icosahedron given Surface-to-volume ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
length_edge = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*surface to volume ratio)
a = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*r)
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
surface to volume ratio - surface to volume ratio is fraction of surface to volume. (Measured in Hundred)
STEP 1: Convert Input(s) to Base Unit
surface to volume ratio: 0.5 Hundred --> 0.5 Hundred No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
a = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*r) --> (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*0.5)
Evaluating ... ...
a = 12.8455952318312
STEP 3: Convert Result to Output's Unit
12.8455952318312 Meter --> No Conversion Required
FINAL ANSWER
12.8455952318312 Meter <-- Length of edge
(Calculation completed in 00.015 seconds)

11 Other formulas that you can solve using the same Inputs

volume of Rhombic Dodecahedron given Surface-to-volume ratio
volume = (16/9)*sqrt(3)*((9*sqrt(2))/(2*sqrt(3)*surface to volume ratio))^3 Go
Volume of triakis tetrahedron given surface-volume-ratio
volume = (3/20)*sqrt(2)*((4*sqrt(11))/(surface to volume ratio*sqrt(2)))^3 Go
side given Surface-to-volume ratio (A/V) of Rhombic Triacontahedron
side = (3*sqrt(5))/(surface to volume ratio*(sqrt(5+(2*sqrt(5))))) Go
height of triakis tetrahedron given surface-volime-ratio
height = (3/5)*(sqrt(6))*(4/surface to volume ratio)*(sqrt(11/2)) Go
edge length of Rhombic Dodecahedron given Surface-to-volume ratio
side_a = (9*sqrt(2))/(2*sqrt(3)*surface to volume ratio) Go
edge length of tetrahedron(a) of triakis tetrahedron given Surface-to-volume ratio (A/V)
side_a = (4*sqrt(11))/(surface to volume ratio*sqrt(2)) Go
Area of triakis tetrahedron given surface-volume-ratio
area = (3/5)*(sqrt(11/2))*(4/surface to volume ratio)^2 Go
Area of Rhombic Dodecahedron given Surface-to-volume ratio
area = (108*sqrt(2))/((surface to volume ratio)^2) Go
Midsphere radius of Rhombic Dodecahedron given Surface-to-volume ratio
radius = (6/sqrt(3))*(1/surface to volume ratio) Go
Midsphere radius of triakis tetrahedron given surface-volume-ratio
radius = sqrt(11)/surface to volume ratio Go
Insphere radius of triakis tetrahedron given surface-volume-ratio
radius = 3/surface to volume ratio Go

11 Other formulas that calculate the same Output

Lateral edge length of a Right square pyramid when side length and slant height are given
length_edge = sqrt(Side^2/2+(Slant Height^2-Side^2/4)) Go
Lateral edge length of a Right square pyramid when volume and side length is given
length_edge = sqrt(Side^2/2+((3*Volume)/Side^2)^2) Go
Edge length (a) of Great Dodecahedron given Surface area (A)
length_edge = sqrt(Area/(15*(sqrt(5-2*sqrt(5))))) Go
Edge length (a) of Great Dodecahedron given Pyramid height (hp)
length_edge = (6*Height)/(sqrt(3)*(3-sqrt(5))) Go
Edge length (a) of Great Dodecahedron given Circumsphere radius (rc)
length_edge = (4*Radius)/(sqrt(10+2*sqrt(5))) Go
Lateral edge length of a Right Square pyramid
length_edge = sqrt(Height^2+Length^2/2) Go
Edge length (a) of Great Dodecahedron given Volume (V)
length_edge = ((4*Volume)/(5*(sqrt(5)-1)))^(1/3) Go
Edge length (a) of Great Dodecahedron given Ridge length (s)
length_edge = (2*length 1)/(sqrt(5)-1) Go
Edge of Regular Octahedron
length_edge = (3^(1/4))*sqrt(Area/18) Go
Edge of Tetrahedron
length_edge = sqrt(Area)/3^(1/4) Go
Edge length tetrahedron of truncated tetrahedron
length_edge = 3*Side Go

Edge length of Great Icosahedron given Surface-to-volume ratio Formula

length_edge = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*surface to volume ratio)
a = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*r)

What is Great Icosahedron?

In geometry, the great icosahedron is one of four Kepler–Poinsot polyhedra, with Schläfli symbol {3, ​⁵⁄₂} and Coxeter–Dynkin diagram of. It is composed of 20 intersecting triangular faces, having five triangles meeting at each vertex in a pentagrammic sequence.

How to Calculate Edge length of Great Icosahedron given Surface-to-volume ratio?

Edge length of Great Icosahedron given Surface-to-volume ratio calculator uses length_edge = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*surface to volume ratio) to calculate the Length of edge, The Edge length of Great Icosahedron given Surface-to-volume ratio formula is defined as a straight line connecting two vertices of Great Icosahedron. Length of edge and is denoted by a symbol.

How to calculate Edge length of Great Icosahedron given Surface-to-volume ratio using this online calculator? To use this online calculator for Edge length of Great Icosahedron given Surface-to-volume ratio, enter surface to volume ratio (r) and hit the calculate button. Here is how the Edge length of Great Icosahedron given Surface-to-volume ratio calculation can be explained with given input values -> 12.8456 = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*0.5).

FAQ

What is Edge length of Great Icosahedron given Surface-to-volume ratio?
The Edge length of Great Icosahedron given Surface-to-volume ratio formula is defined as a straight line connecting two vertices of Great Icosahedron and is represented as a = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*r) or length_edge = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*surface to volume ratio). surface to volume ratio is fraction of surface to volume.
How to calculate Edge length of Great Icosahedron given Surface-to-volume ratio?
The Edge length of Great Icosahedron given Surface-to-volume ratio formula is defined as a straight line connecting two vertices of Great Icosahedron is calculated using length_edge = (3*sqrt(3)*(5+4*sqrt(5)))/((1/4)*(25+9*sqrt(5))*surface to volume ratio). To calculate Edge length of Great Icosahedron given Surface-to-volume ratio, you need surface to volume ratio (r). With our tool, you need to enter the respective value for surface to volume ratio 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 Length of edge?
In this formula, Length of edge uses surface to volume ratio. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • length_edge = sqrt(Height^2+Length^2/2)
  • length_edge = sqrt(Side^2/2+(Slant Height^2-Side^2/4))
  • length_edge = sqrt(Side^2/2+((3*Volume)/Side^2)^2)
  • length_edge = sqrt(Area)/3^(1/4)
  • length_edge = (3^(1/4))*sqrt(Area/18)
  • length_edge = 3*Side
  • length_edge = (2*length 1)/(sqrt(5)-1)
  • length_edge = (4*Radius)/(sqrt(10+2*sqrt(5)))
  • length_edge = (6*Height)/(sqrt(3)*(3-sqrt(5)))
  • length_edge = sqrt(Area/(15*(sqrt(5-2*sqrt(5)))))
  • length_edge = ((4*Volume)/(5*(sqrt(5)-1)))^(1/3)
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