Face Area of Dodecahedron given Surface to Volume Ratio Calculator

✖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 [R_A/V]

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✖The Face Area of Dodecahedron is the amount of space occupied by any one of the 12 faces of Dodecahedron.ⓘ Face Area of Dodecahedron given Surface to Volume Ratio [A_Face]

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Face Area of Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2
A_Face = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(R_A/V*(15+(7*sqrt(5)))))^2
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

Face Area of Dodecahedron - (Measured in Square Meter) - The Face Area of Dodecahedron is the amount of space occupied by any one of the 12 faces of Dodecahedron.
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.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Dodecahedron: 0.3 1 per Meter --> 0.3 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_Face = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(R_A/V*(15+(7*sqrt(5)))))^2 --> 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(0.3*(15+(7*sqrt(5)))))^2

Evaluating ... ...

A_Face = 138.757275712888

STEP 3: Convert Result to Output's Unit

138.757275712888 Square Meter --> No Conversion Required

FINAL ANSWER

138.757275712888 ≈ 138.7573 Square Meter <-- Face Area of Dodecahedron

(Calculation completed in 00.020 seconds)

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< Face Area of Dodecahedron Calculators

Face Area of Dodecahedron given Circumsphere Radius

LaTeX Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2

Face Area of Dodecahedron given Face Diagonal

LaTeX Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2

Face Area of Dodecahedron

LaTeX Go Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2

Face Area of Dodecahedron given Total Surface Area

LaTeX Go Face Area of Dodecahedron = Total Surface Area of Dodecahedron/12

Face Area of Dodecahedron given Surface to Volume Ratio 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 Face Area of Dodecahedron given Surface to Volume Ratio?

Face Area of Dodecahedron given Surface to Volume Ratio calculator uses Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2 to calculate the Face Area of Dodecahedron, The Face Area of Dodecahedron given Surface to Volume Ratio formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron, and calculated using surface to volume ratio of Dodecahedron. Face Area of Dodecahedron is denoted by A_Face symbol.

How to calculate Face Area of Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Face Area of Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Dodecahedron (R_A/V) and hit the calculate button. Here is how the Face Area of Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 138.7573 = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(0.3*(15+(7*sqrt(5)))))^2.

FAQ

What is Face Area of Dodecahedron given Surface to Volume Ratio?

The Face Area of Dodecahedron given Surface to Volume Ratio formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron, and calculated using surface to volume ratio of Dodecahedron and is represented as A_Face = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(R_A/V*(15+(7*sqrt(5)))))^2 or Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2. The Surface to Volume Ratio of Dodecahedron is the numerical ratio of the total surface area to the volume of the Dodecahedron.

How to calculate Face Area of Dodecahedron given Surface to Volume Ratio?

The Face Area of Dodecahedron given Surface to Volume Ratio formula is defined as the amount of space occupied by any one of the 12 faces of Dodecahedron, and calculated using surface to volume ratio of Dodecahedron is calculated using Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2. To calculate Face Area of Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Dodecahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Face Area of Dodecahedron?

In this formula, Face Area of Dodecahedron uses Surface to Volume Ratio of Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Face Area of Dodecahedron = Total Surface Area of Dodecahedron/12

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