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Surface-to-volume ratio (A/V) of Great Dodecahedron given Circumsphere radius (rc) Solution

STEP 0: Pre-Calculation Summary
Formula Used
surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(10+2*sqrt(5)))/(4*Radius))
r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(10+2*sqrt(5)))/(4*r))
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Radius - Radius is a radial line from the focus to any point of a curve. (Measured in Centimeter)
STEP 1: Convert Input(s) to Base Unit
Radius: 18 Centimeter --> 0.18 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(10+2*sqrt(5)))/(4*r)) --> ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(10+2*sqrt(5)))/(4*0.18))
Evaluating ... ...
r = 37.2677996249965
STEP 3: Convert Result to Output's Unit
37.2677996249965 Hundred --> No Conversion Required
FINAL ANSWER
37.2677996249965 Hundred <-- surface to volume ratio
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

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
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
Volume of a Circular Cone
volume = (1/3)*pi*(Radius)^2*Height Go
Volume of a Circular Cylinder
volume = pi*(Radius)^2*Height Go
Base Surface Area of a Cone
base_surface_area = pi*Radius^2 Go
Top Surface Area of a Cylinder
top_surface_area = pi*Radius^2 Go
Area of a Circle when radius is given
area_of_circle = pi*Radius^2 Go
Volume of a Hemisphere
volume = (2/3)*pi*(Radius)^3 Go
Volume of a Sphere
volume = (4/3)*pi*(Radius)^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 Circumsphere radius (rc) Formula

surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(10+2*sqrt(5)))/(4*Radius))
r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(10+2*sqrt(5)))/(4*r))

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 Circumsphere radius (rc)?

Surface-to-volume ratio (A/V) of Great Dodecahedron given Circumsphere radius (rc) calculator uses surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(10+2*sqrt(5)))/(4*Radius)) to calculate the surface to volume ratio, The Surface-to-volume ratio (A/V) of Great Dodecahedron given Circumsphere radius (rc) 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 Circumsphere radius (rc) using this online calculator? To use this online calculator for Surface-to-volume ratio (A/V) of Great Dodecahedron given Circumsphere radius (rc), enter Radius (r) and hit the calculate button. Here is how the Surface-to-volume ratio (A/V) of Great Dodecahedron given Circumsphere radius (rc) calculation can be explained with given input values -> 37.2678 = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(10+2*sqrt(5)))/(4*0.18)).

FAQ

What is Surface-to-volume ratio (A/V) of Great Dodecahedron given Circumsphere radius (rc)?
The Surface-to-volume ratio (A/V) of Great Dodecahedron given Circumsphere radius (rc) 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)))*((sqrt(10+2*sqrt(5)))/(4*r)) or surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*((sqrt(10+2*sqrt(5)))/(4*Radius)). Radius is a radial line from the focus to any point of a curve.
How to calculate Surface-to-volume ratio (A/V) of Great Dodecahedron given Circumsphere radius (rc)?
The Surface-to-volume ratio (A/V) of Great Dodecahedron given Circumsphere radius (rc) 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)))*((sqrt(10+2*sqrt(5)))/(4*Radius)). To calculate Surface-to-volume ratio (A/V) of Great Dodecahedron given Circumsphere radius (rc), you need Radius (r). With our tool, you need to enter the respective value for Radius 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 Radius. 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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