Total Surface Area of Pentagonal Hexecontahedron given Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Pentagonal Hexecontahedron = 30*((Volume of Pentagonal Hexecontahedron*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
TSA = 30*((V*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
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
Total Surface Area of Pentagonal Hexecontahedron - (Measured in Square Meter) - Total Surface Area of Pentagonal Hexecontahedron is the amount or quantity of two dimensional space covered on the surface of Pentagonal Hexecontahedron.
Volume of Pentagonal Hexecontahedron - (Measured in Cubic Meter) - Volume of Pentagonal Hexecontahedron is the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron.
STEP 1: Convert Input(s) to Base Unit
Volume of Pentagonal Hexecontahedron: 12000 Cubic Meter --> 12000 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = 30*((V*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2) --> 30*((12000*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
Evaluating ... ...
TSA = 2582.20334910529
STEP 3: Convert Result to Output's Unit
2582.20334910529 Square Meter --> No Conversion Required
FINAL ANSWER
2582.20334910529 2582.203 Square Meter <-- Total Surface Area of Pentagonal Hexecontahedron
(Calculation completed in 00.004 seconds)

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7 Surface Area of Pentagonal Hexecontahedron Calculators

Total Surface Area of Pentagonal Hexecontahedron given Long Edge
Go Total Surface Area of Pentagonal Hexecontahedron = 30*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
Total Surface Area of Pentagonal Hexecontahedron given Surface to Volume Ratio
Go Total Surface Area of Pentagonal Hexecontahedron = 30*((6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
Total Surface Area of Pentagonal Hexecontahedron given Volume
Go Total Surface Area of Pentagonal Hexecontahedron = 30*((Volume of Pentagonal Hexecontahedron*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius
Go Total Surface Area of Pentagonal Hexecontahedron = 30*((Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
Total Surface Area of Pentagonal Hexecontahedron given Midsphere Radius
Go Total Surface Area of Pentagonal Hexecontahedron = 30*(Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
Total Surface Area of Pentagonal Hexecontahedron given Snub Dodecahedron Edge
Go Total Surface Area of Pentagonal Hexecontahedron = 30*(Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
Total Surface Area of Pentagonal Hexecontahedron
Go Total Surface Area of Pentagonal Hexecontahedron = 30*Short Edge of Pentagonal Hexecontahedron^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)

Total Surface Area of Pentagonal Hexecontahedron given Volume Formula

Total Surface Area of Pentagonal Hexecontahedron = 30*((Volume of Pentagonal Hexecontahedron*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
TSA = 30*((V*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)

What is Pentagonal Hexecontahedron?

In geometry, a Pentagonal Hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. It has 60 faces, 150 edges, 92 vertices. It is the Catalan solid with the most vertices. Among the Catalan and Archimedean solids, it has the second largest number of vertices, after the truncated icosidodecahedron, which has 120 vertices.

How to Calculate Total Surface Area of Pentagonal Hexecontahedron given Volume?

Total Surface Area of Pentagonal Hexecontahedron given Volume calculator uses Total Surface Area of Pentagonal Hexecontahedron = 30*((Volume of Pentagonal Hexecontahedron*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2) to calculate the Total Surface Area of Pentagonal Hexecontahedron, Total Surface Area of Pentagonal Hexecontahedron given Volume formula is defined as the amount or quantity of two-dimensional space covered by the surface of the Pentagonal Hexecontahedron, calculated using the volume of the Pentagonal Hexecontahedron. Total Surface Area of Pentagonal Hexecontahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Pentagonal Hexecontahedron given Volume using this online calculator? To use this online calculator for Total Surface Area of Pentagonal Hexecontahedron given Volume, enter Volume of Pentagonal Hexecontahedron (V) and hit the calculate button. Here is how the Total Surface Area of Pentagonal Hexecontahedron given Volume calculation can be explained with given input values -> 2582.203 = 30*((12000*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2).

FAQ

What is Total Surface Area of Pentagonal Hexecontahedron given Volume?
Total Surface Area of Pentagonal Hexecontahedron given Volume formula is defined as the amount or quantity of two-dimensional space covered by the surface of the Pentagonal Hexecontahedron, calculated using the volume of the Pentagonal Hexecontahedron and is represented as TSA = 30*((V*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2) or Total Surface Area of Pentagonal Hexecontahedron = 30*((Volume of Pentagonal Hexecontahedron*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2). Volume of Pentagonal Hexecontahedron is the quantity of three dimensional space enclosed by the entire surface of Pentagonal Hexecontahedron.
How to calculate Total Surface Area of Pentagonal Hexecontahedron given Volume?
Total Surface Area of Pentagonal Hexecontahedron given Volume formula is defined as the amount or quantity of two-dimensional space covered by the surface of the Pentagonal Hexecontahedron, calculated using the volume of the Pentagonal Hexecontahedron is calculated using Total Surface Area of Pentagonal Hexecontahedron = 30*((Volume of Pentagonal Hexecontahedron*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)) )^(2/3)*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2). To calculate Total Surface Area of Pentagonal Hexecontahedron given Volume, you need Volume of Pentagonal Hexecontahedron (V). With our tool, you need to enter the respective value for Volume of Pentagonal Hexecontahedron 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 Pentagonal Hexecontahedron?
In this formula, Total Surface Area of Pentagonal Hexecontahedron uses Volume of Pentagonal Hexecontahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Total Surface Area of Pentagonal Hexecontahedron = 30*((31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
  • Total Surface Area of Pentagonal Hexecontahedron = 30*Short Edge of Pentagonal Hexecontahedron^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
  • Total Surface Area of Pentagonal Hexecontahedron = 30*(Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756)))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
  • Total Surface Area of Pentagonal Hexecontahedron = 30*(Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
  • Total Surface Area of Pentagonal Hexecontahedron = 30*((Insphere Radius of Pentagonal Hexecontahedron*2)/(sqrt((1+0.4715756)/((1-0.4715756)*(1-2*0.4715756)))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
  • Total Surface Area of Pentagonal Hexecontahedron = 30*((6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))))^2*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2)
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