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Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V) Solution

STEP 0: Pre-Calculation Summary
Formula Used
surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(((5*(sqrt(5)-1))/(4*Volume))^(1/3))
r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(((5*(sqrt(5)-1))/(4*V))^(1/3))
This formula uses 1 Functions, 1 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Volume - Volume is the amount of space that a substance or object occupies or that is enclosed within a container. (Measured in Cubic Meter)
STEP 1: Convert Input(s) to Base Unit
Volume: 63 Cubic Meter --> 63 Cubic 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)))*(((5*(sqrt(5)-1))/(4*V))^(1/3)) --> ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(((5*(sqrt(5)-1))/(4*63))^(1/3))
Evaluating ... ...
r = 2.04929212426288
STEP 3: Convert Result to Output's Unit
2.04929212426288 Hundred --> No Conversion Required
FINAL ANSWER
2.04929212426288 Hundred <-- surface to volume ratio
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

Slant height of a Right square pyramid when volume and side length are given
slant_height = sqrt((Side^2/4)+((3*Volume)/Side^2)^2) 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
Specific Weight
specific_weight = Weight of body on which frictional force is applied/Volume Go
Height of a triangular prism when base and volume are given
height = (2*Volume)/(Base*Length) Go
Side length of a Right square pyramid when volume and height are given
side = sqrt((3*Volume)/Height) Go
Bottom surface area of a triangular prism when volume and height are given
bottom_surface_area = Volume/Height Go
Body Force Work Rate
body_force_work_rate = Force/Volume Go
Top surface area of a triangular prism when volume and height are given
top_surface_area = Volume/Height Go
Specific Volume
specific_volume = Volume/Mass Go
Height of a right square pyramid when volume and side length are given
height = (3*Volume)/Side^2 Go
Density
density = Mass/Volume 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 Volume (V) Formula

surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(((5*(sqrt(5)-1))/(4*Volume))^(1/3))
r = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(((5*(sqrt(5)-1))/(4*V))^(1/3))

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 Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V)?

Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V) calculator uses surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(((5*(sqrt(5)-1))/(4*Volume))^(1/3)) to calculate the surface to volume ratio, The Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V) 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 Volume (V) using this online calculator? To use this online calculator for Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V), enter Volume (V) and hit the calculate button. Here is how the Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V) calculation can be explained with given input values -> 2.049292 = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(((5*(sqrt(5)-1))/(4*63))^(1/3)).

FAQ

What is Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V)?
The Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V) 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)))*(((5*(sqrt(5)-1))/(4*V))^(1/3)) or surface_to_volume_ratio = ((15*(sqrt(5-2*sqrt(5))))/((5/4)*(sqrt(5)-1)))*(((5*(sqrt(5)-1))/(4*Volume))^(1/3)). Volume is the amount of space that a substance or object occupies or that is enclosed within a container.
How to calculate Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V)?
The Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V) 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)))*(((5*(sqrt(5)-1))/(4*Volume))^(1/3)). To calculate Surface-to-volume ratio (A/V) of Great Dodecahedron given Volume (V), you need Volume (V). With our tool, you need to enter the respective value for Volume 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 Volume. 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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