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Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a) Solution

STEP 0: Pre-Calculation Summary
Formula Used
surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/Side)
r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/s)
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
r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/s) --> ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/9)
Evaluating ... ...
r = 0.783713669723297
STEP 3: Convert Result to Output's Unit
0.783713669723297 Hundred --> No Conversion Required
FINAL ANSWER
0.783713669723297 Hundred <-- surface to volume ratio
(Calculation completed in 00.031 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

surface-volume-ratio of triakis tetrahedron given area
surface_to_volume_ratio = 4*(sqrt(11/2))*(sqrt((3*sqrt(11))/(5*Area))) Go
Surface-to-volume ratio (A/V) given side of Rhombic Triacontahedron
surface_to_volume_ratio = (3*sqrt(5))/(Side*(sqrt(5+(2*sqrt(5))))) Go
surface-volume-ratio of triakis tetrahedron given volume
surface_to_volume_ratio = 4*(sqrt(11/2))*(((3*sqrt(2))/(20*Volume))^(1/3)) Go
surface-volume-ratio of triakis tetrahedron given height
surface_to_volume_ratio = 4*(sqrt(11/2))*((3*sqrt(6))/(5*Height)) Go
Surface-to-volume ratio of Rhombic Dodecahedron given edge length
surface_to_volume_ratio = (9*sqrt(2))/(2*sqrt(3)*Side A) Go
Surface-to-volume ratio (A/V) of triakis tetrahedron given edge length of tetrahedron(a)
surface_to_volume_ratio = (4*sqrt(11))/(Side A*sqrt(2)) Go
surface-volume-ratio of triakis tetrahedron given Edge length of pyramid(b)
surface_to_volume_ratio = 4*(sqrt(11/2))*(3/(5*Side B)) Go
Surface-to-volume ratio of Rhombic Dodecahedron given Midsphere radius
surface_to_volume_ratio = (6/(sqrt(3)*Radius)) Go
surface-volume-ratio of triakis tetrahedron given Midsphere radius
surface_to_volume_ratio = sqrt(11)/Radius Go
Surface-to-volume ratio of Rhombic Dodecahedron given Insphere radius
surface_to_volume_ratio = (3/Radius) Go
surface-volume-ratio of triakis tetrahedron given Insphere radius
surface_to_volume_ratio = 3/Radius Go

Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a) Formula

surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/Side)
r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/s)

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 Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a)?

Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a) calculator uses surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/Side) to calculate the surface to volume ratio, The Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a) formula is defined as what part of total volume of Great Dodecahedron is its total surface area. surface to volume ratio and is denoted by r symbol.

How to calculate Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a) using this online calculator? To use this online calculator for Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a), enter Side (s) and hit the calculate button. Here is how the Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a) calculation can be explained with given input values -> 0.783714 = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/9).

FAQ

What is Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a)?
The Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a) formula is defined as what part of total volume of Great Dodecahedron is its total surface area and is represented as r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/s) or surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/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.
How to calculate Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a)?
The Surface-to-volume ratio (A/V) of Great Dodecahedron given Edge length (a) formula is defined as what part of total volume of Great Dodecahedron is its total surface area is calculated using surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(1/Side). To calculate Surface-to-volume ratio (A/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 surface to volume ratio?
In this formula, surface to volume ratio uses Side. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • surface_to_volume_ratio = (3*sqrt(5))/(Side*(sqrt(5+(2*sqrt(5)))))
  • surface_to_volume_ratio = (4*sqrt(11))/(Side A*sqrt(2))
  • surface_to_volume_ratio = 4*(sqrt(11/2))*(3/(5*Side B))
  • surface_to_volume_ratio = 4*(sqrt(11/2))*((3*sqrt(6))/(5*Height))
  • surface_to_volume_ratio = 4*(sqrt(11/2))*(sqrt((3*sqrt(11))/(5*Area)))
  • surface_to_volume_ratio = 3/Radius
  • surface_to_volume_ratio = sqrt(11)/Radius
  • surface_to_volume_ratio = 4*(sqrt(11/2))*(((3*sqrt(2))/(20*Volume))^(1/3))
  • surface_to_volume_ratio = (9*sqrt(2))/(2*sqrt(3)*Side A)
  • surface_to_volume_ratio = (3/Radius)
  • surface_to_volume_ratio = (6/(sqrt(3)*Radius))
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