Surface to Volume Ratio of Dodecahedron given Insphere Radius Calculator

✖Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.ⓘ Insphere Radius of Dodecahedron [r_i]

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✖The Surface to Volume Ratio of Dodecahedron is the numerical ratio of the total surface area to the volume of the Dodecahedron.ⓘ Surface to Volume Ratio of Dodecahedron given Insphere Radius [R_A/V]

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Surface to Volume Ratio of Dodecahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
R_A/V = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(r_i*(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.
Insphere Radius of Dodecahedron - (Measured in Meter) - Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Dodecahedron: 11 Meter --> 11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(r_i*(15+(7*sqrt(5)))) --> sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(11*(15+(7*sqrt(5))))

Evaluating ... ...

R_A/V = 0.272727272727273

STEP 3: Convert Result to Output's Unit

0.272727272727273 1 per Meter --> No Conversion Required

FINAL ANSWER

0.272727272727273 ≈ 0.272727 1 per Meter <-- Surface to Volume Ratio of Dodecahedron

(Calculation completed in 00.004 seconds)

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< Surface to Volume Ratio of Dodecahedron Calculators

Surface to Volume Ratio of Dodecahedron given Total Surface Area

LaTeX 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

LaTeX 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 Volume

LaTeX 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

LaTeX 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 Insphere Radius Formula

LaTeX Go

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 Insphere Radius?

Surface to Volume Ratio of Dodecahedron given Insphere Radius calculator uses 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)))) to calculate the Surface to Volume Ratio of Dodecahedron, The Surface to Volume Ratio of Dodecahedron given Insphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Dodecahedron and calculated using the insphere radius of the Dodecahedron. Surface to Volume Ratio of Dodecahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Dodecahedron given Insphere Radius, enter Insphere Radius of Dodecahedron (r_i) and hit the calculate button. Here is how the Surface to Volume Ratio of Dodecahedron given Insphere Radius calculation can be explained with given input values -> 0.272727 = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(11*(15+(7*sqrt(5)))).

FAQ

What is Surface to Volume Ratio of Dodecahedron given Insphere Radius?

The Surface to Volume Ratio of Dodecahedron given Insphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Dodecahedron and calculated using the insphere radius of the Dodecahedron and is represented as R_A/V = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(r_i*(15+(7*sqrt(5)))) or 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)))). Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.

How to calculate Surface to Volume Ratio of Dodecahedron given Insphere Radius?

The Surface to Volume Ratio of Dodecahedron given Insphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Dodecahedron and calculated using the insphere radius of the Dodecahedron is calculated using 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)))). To calculate Surface to Volume Ratio of Dodecahedron given Insphere Radius, you need Insphere Radius of Dodecahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius 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 Insphere Radius of Dodecahedron. We can use 3 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)))

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