Surface to Volume Ratio of Dodecahedron given Perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Surface to Volume Ratio of Dodecahedron = (360*sqrt(25+(10*sqrt(5))))/(Perimeter of Dodecahedron*(15+(7*sqrt(5))))
RA/V = (360*sqrt(25+(10*sqrt(5))))/(P*(15+(7*sqrt(5))))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Surface to Volume Ratio of Dodecahedron - (Measured in 1 per Meter) - The Surface to Volume Ratio of Dodecahedron is the numerical ratio of the total surface area to the volume of the Dodecahedron.
Perimeter of Dodecahedron - (Measured in Meter) - Perimeter of Dodecahedron is the sum of the total distance around all the edges of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Perimeter of Dodecahedron: 300 Meter --> 300 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RA/V = (360*sqrt(25+(10*sqrt(5))))/(P*(15+(7*sqrt(5)))) --> (360*sqrt(25+(10*sqrt(5))))/(300*(15+(7*sqrt(5))))
Evaluating ... ...
RA/V = 0.269416785947751
STEP 3: Convert Result to Output's Unit
0.269416785947751 1 per Meter --> No Conversion Required
FINAL ANSWER
0.269416785947751 0.269417 1 per Meter <-- Surface to Volume Ratio of Dodecahedron
(Calculation completed in 00.021 seconds)

Credits

Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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12 Surface to Volume Ratio of Dodecahedron Calculators

Surface to Volume Ratio of Dodecahedron given Lateral Surface Area
Go Surface to Volume Ratio of Dodecahedron = sqrt((5*sqrt(25+(10*sqrt(5))))/(2*Lateral Surface Area of Dodecahedron))*(12*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
Surface to Volume Ratio of Dodecahedron given Total Surface Area
Go Surface to Volume Ratio of Dodecahedron = sqrt((3*sqrt(25+(10*sqrt(5))))/Total Surface Area of Dodecahedron)*(12*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
Surface to Volume Ratio of Dodecahedron given Face Area
Go Surface to Volume Ratio of Dodecahedron = sqrt(sqrt(25+(10*sqrt(5)))/(4*Face Area of Dodecahedron))*(12*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
Surface to Volume Ratio of Dodecahedron given Insphere Radius
Go Surface to Volume Ratio of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(Insphere Radius of Dodecahedron*(15+(7*sqrt(5))))
Surface to Volume Ratio of Dodecahedron given Circumsphere Radius
Go Surface to Volume Ratio of Dodecahedron = (sqrt(3)*(1+sqrt(5)))/Circumsphere Radius of Dodecahedron*(3*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
Surface to Volume Ratio of Dodecahedron given Space Diagonal
Go Surface to Volume Ratio of Dodecahedron = (sqrt(3)*(1+sqrt(5)))/Space Diagonal of Dodecahedron*(6*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
Surface to Volume Ratio of Dodecahedron given Volume
Go Surface to Volume Ratio of Dodecahedron = ((15+(7*sqrt(5)))/(4*Volume of Dodecahedron))^(1/3)*(12*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
Surface to Volume Ratio of Dodecahedron given Midsphere Radius
Go Surface to Volume Ratio of Dodecahedron = (3+sqrt(5))/Midsphere Radius of Dodecahedron* (3*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
Surface to Volume Ratio of Dodecahedron given Face Diagonal
Go Surface to Volume Ratio of Dodecahedron = (1+sqrt(5))/Face Diagonal of Dodecahedron*(6*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
Surface to Volume Ratio of Dodecahedron given Face Perimeter
Go Surface to Volume Ratio of Dodecahedron = (60*sqrt(25+(10*sqrt(5))))/((15+(7*sqrt(5)))*Face Perimeter of Dodecahedron)
Surface to Volume Ratio of Dodecahedron
Go Surface to Volume Ratio of Dodecahedron = (12*sqrt(25+(10*sqrt(5))))/(Edge Length of Dodecahedron*(15+(7*sqrt(5))))
Surface to Volume Ratio of Dodecahedron given Perimeter
Go Surface to Volume Ratio of Dodecahedron = (360*sqrt(25+(10*sqrt(5))))/(Perimeter of Dodecahedron*(15+(7*sqrt(5))))

Surface to Volume Ratio of Dodecahedron given Perimeter Formula

Surface to Volume Ratio of Dodecahedron = (360*sqrt(25+(10*sqrt(5))))/(Perimeter of Dodecahedron*(15+(7*sqrt(5))))
RA/V = (360*sqrt(25+(10*sqrt(5))))/(P*(15+(7*sqrt(5))))

What is a Dodecahedron?

A Dodecahedron is a symmetric and closed three dimensional shape with 12 identical pentagonal faces. It is a Platonic solid, which has 12 faces, 20 vertices and 30 edges. At each vertex, three pentagonal faces meet and at each edge, two pentagonal faces meet. Out of all the five Platonic solids with identical edge length, Dodecahedron will have the highest value of volume and surface area.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Surface to Volume Ratio of Dodecahedron given Perimeter?

Surface to Volume Ratio of Dodecahedron given Perimeter calculator uses Surface to Volume Ratio of Dodecahedron = (360*sqrt(25+(10*sqrt(5))))/(Perimeter of Dodecahedron*(15+(7*sqrt(5)))) to calculate the Surface to Volume Ratio of Dodecahedron, The Surface to Volume Ratio of Dodecahedron given Perimeter formula is defined as the numerical ratio of the total surface area to the volume of the Dodecahedron and calculated using the perimeter of the Dodecahedron. Surface to Volume Ratio of Dodecahedron is denoted by RA/V symbol.

How to calculate Surface to Volume Ratio of Dodecahedron given Perimeter using this online calculator? To use this online calculator for Surface to Volume Ratio of Dodecahedron given Perimeter, enter Perimeter of Dodecahedron (P) and hit the calculate button. Here is how the Surface to Volume Ratio of Dodecahedron given Perimeter calculation can be explained with given input values -> 0.269417 = (360*sqrt(25+(10*sqrt(5))))/(300*(15+(7*sqrt(5)))).

FAQ

What is Surface to Volume Ratio of Dodecahedron given Perimeter?
The Surface to Volume Ratio of Dodecahedron given Perimeter formula is defined as the numerical ratio of the total surface area to the volume of the Dodecahedron and calculated using the perimeter of the Dodecahedron and is represented as RA/V = (360*sqrt(25+(10*sqrt(5))))/(P*(15+(7*sqrt(5)))) or Surface to Volume Ratio of Dodecahedron = (360*sqrt(25+(10*sqrt(5))))/(Perimeter of Dodecahedron*(15+(7*sqrt(5)))). Perimeter of Dodecahedron is the sum of the total distance around all the edges of the Dodecahedron.
How to calculate Surface to Volume Ratio of Dodecahedron given Perimeter?
The Surface to Volume Ratio of Dodecahedron given Perimeter formula is defined as the numerical ratio of the total surface area to the volume of the Dodecahedron and calculated using the perimeter of the Dodecahedron is calculated using Surface to Volume Ratio of Dodecahedron = (360*sqrt(25+(10*sqrt(5))))/(Perimeter of Dodecahedron*(15+(7*sqrt(5)))). To calculate Surface to Volume Ratio of Dodecahedron given Perimeter, you need Perimeter of Dodecahedron (P). With our tool, you need to enter the respective value for Perimeter of Dodecahedron 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 of Dodecahedron?
In this formula, Surface to Volume Ratio of Dodecahedron uses Perimeter of Dodecahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • Surface to Volume Ratio of Dodecahedron = (12*sqrt(25+(10*sqrt(5))))/(Edge Length of Dodecahedron*(15+(7*sqrt(5))))
  • Surface to Volume Ratio of Dodecahedron = ((15+(7*sqrt(5)))/(4*Volume of Dodecahedron))^(1/3)*(12*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
  • Surface to Volume Ratio of Dodecahedron = sqrt((3*sqrt(25+(10*sqrt(5))))/Total Surface Area of Dodecahedron)*(12*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
  • Surface to Volume Ratio of Dodecahedron = sqrt(sqrt(25+(10*sqrt(5)))/(4*Face Area of Dodecahedron))*(12*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
  • Surface to Volume Ratio of Dodecahedron = (sqrt(3)*(1+sqrt(5)))/Circumsphere Radius of Dodecahedron*(3*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
  • Surface to Volume Ratio of Dodecahedron = (60*sqrt(25+(10*sqrt(5))))/((15+(7*sqrt(5)))*Face Perimeter of Dodecahedron)
  • Surface to Volume Ratio of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(Insphere Radius of Dodecahedron*(15+(7*sqrt(5))))
  • Surface to Volume Ratio of Dodecahedron = (3+sqrt(5))/Midsphere Radius of Dodecahedron* (3*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
  • Surface to Volume Ratio of Dodecahedron = (1+sqrt(5))/Face Diagonal of Dodecahedron*(6*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
  • Surface to Volume Ratio of Dodecahedron = (sqrt(3)*(1+sqrt(5)))/Space Diagonal of Dodecahedron*(6*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
  • Surface to Volume Ratio of Dodecahedron = sqrt((5*sqrt(25+(10*sqrt(5))))/(2*Lateral Surface Area of Dodecahedron))*(12*sqrt(25+(10*sqrt(5))))/(15+(7*sqrt(5)))
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