## Total Surface Area of Dodecahedron given Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
TSA = 3*sqrt(25+(10*sqrt(5)))*((4*V)/(15+(7*sqrt(5))))^(2/3)
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Total Surface Area of Dodecahedron - (Measured in Square Meter) - Total Surface Area of Dodecahedron is the total quantity of plane enclosed by the entire surface of the Dodecahedron.
Volume of Dodecahedron - (Measured in Cubic Meter) - Volume of Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Volume of Dodecahedron: 7700 Cubic Meter --> 7700 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = 3*sqrt(25+(10*sqrt(5)))*((4*V)/(15+(7*sqrt(5))))^(2/3) --> 3*sqrt(25+(10*sqrt(5)))*((4*7700)/(15+(7*sqrt(5))))^(2/3)
Evaluating ... ...
TSA = 2071.19182590782
STEP 3: Convert Result to Output's Unit
2071.19182590782 Square Meter --> No Conversion Required
2071.19182590782 2071.192 Square Meter <-- Total Surface Area of Dodecahedron
(Calculation completed in 00.004 seconds)
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## < 12 Total Surface Area of Dodecahedron Calculators

Total Surface Area of Dodecahedron given Surface to Volume Ratio
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2
Total Surface Area of Dodecahedron given Insphere Radius
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2
Total Surface Area of Dodecahedron given Circumsphere Radius
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Total Surface Area of Dodecahedron given Space Diagonal
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Total Surface Area of Dodecahedron given Midsphere Radius
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
Total Surface Area of Dodecahedron given Volume
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
Total Surface Area of Dodecahedron given Face Diagonal
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
Total Surface Area of Dodecahedron given Face Perimeter
Total Surface Area of Dodecahedron = 3/25*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
Total Surface Area of Dodecahedron given Perimeter
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*(Perimeter of Dodecahedron/30)^2
Total Surface Area of Dodecahedron
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Total Surface Area of Dodecahedron given Lateral Surface Area
Total Surface Area of Dodecahedron = 6/5*Lateral Surface Area of Dodecahedron
Total Surface Area of Dodecahedron given Face Area
Total Surface Area of Dodecahedron = 12*Face Area of Dodecahedron

## < 8 Area of Dodecahedron Calculators

Lateral Surface Area of Dodecahedron given Circumsphere Radius
Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
Total Surface Area of Dodecahedron given Volume
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
Face Area of Dodecahedron given Midsphere Radius
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
Total Surface Area of Dodecahedron given Face Perimeter
Total Surface Area of Dodecahedron = 3/25*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
Lateral Surface Area of Dodecahedron
Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Total Surface Area of Dodecahedron
Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Face Area of Dodecahedron
Face Area of Dodecahedron = 1/4*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Lateral Surface Area of Dodecahedron given Total Surface Area
Lateral Surface Area of Dodecahedron = 5/6*Total Surface Area of Dodecahedron

## Total Surface Area of Dodecahedron given Volume Formula

Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
TSA = 3*sqrt(25+(10*sqrt(5)))*((4*V)/(15+(7*sqrt(5))))^(2/3)

## 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 Total Surface Area of Dodecahedron given Volume?

Total Surface Area of Dodecahedron given Volume calculator uses Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3) to calculate the Total Surface Area of Dodecahedron, The Total Surface Area of Dodecahedron given Volume formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron, and calculated using volume of Dodecahedron. Total Surface Area of Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Dodecahedron given Volume using this online calculator? To use this online calculator for Total Surface Area of Dodecahedron given Volume, enter Volume of Dodecahedron (V) and hit the calculate button. Here is how the Total Surface Area of Dodecahedron given Volume calculation can be explained with given input values -> 2071.192 = 3*sqrt(25+(10*sqrt(5)))*((4*7700)/(15+(7*sqrt(5))))^(2/3).

### FAQ

What is Total Surface Area of Dodecahedron given Volume?
The Total Surface Area of Dodecahedron given Volume formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron, and calculated using volume of Dodecahedron and is represented as TSA = 3*sqrt(25+(10*sqrt(5)))*((4*V)/(15+(7*sqrt(5))))^(2/3) or Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3). Volume of Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Dodecahedron.
How to calculate Total Surface Area of Dodecahedron given Volume?
The Total Surface Area of Dodecahedron given Volume formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron, and calculated using volume of Dodecahedron is calculated using Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3). To calculate Total Surface Area of Dodecahedron given Volume, you need Volume of Dodecahedron (V). With our tool, you need to enter the respective value for Volume 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 Total Surface Area of Dodecahedron?
In this formula, Total Surface Area of Dodecahedron uses Volume of Dodecahedron. We can use 13 other way(s) to calculate the same, which is/are as follows -
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
• Total Surface Area of Dodecahedron = 12*Face Area of Dodecahedron
• Total Surface Area of Dodecahedron = 3/25*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Midsphere Radius of Dodecahedron)/(3+sqrt(5)))^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((12*(sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))))^2
• Total Surface Area of Dodecahedron = 6/5*Lateral Surface Area of Dodecahedron
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*(Perimeter of Dodecahedron/30)^2
• Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
• Total Surface Area of Dodecahedron = 3/25*sqrt(25+(10*sqrt(5)))*Face Perimeter of Dodecahedron^2 Let Others Know