Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius Calculator

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

+10%

-10%

✖Total Surface Area of Pentagonal Hexecontahedron is the amount or quantity of two dimensional space covered on the surface of Pentagonal Hexecontahedron.ⓘ Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius [TSA]

⎘ Copy

👎

Formula

✖

Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius

Formula

`"TSA" = 30*(("r"_{"i"}*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)`

Example

`"2603.889m²"=30*(("14m"*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)`

Calculator

LaTeX

Reset

👍

Download 3D Geometry Formula PDF

Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
TSA = 30*((r_i*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)
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.
Insphere Radius of Pentagonal Hexecontahedron - (Measured in Meter) - Insphere Radius of Pentagonal Hexecontahedron is the radius of the sphere that is contained by the Pentagonal Hexecontahedron in such a way that all the faces just touch the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Pentagonal Hexecontahedron: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 30*((r_i*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) --> 30*((14*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)

Evaluating ... ...

TSA = 2603.88853877871

STEP 3: Convert Result to Output's Unit

2603.88853877871 Square Meter --> No Conversion Required

FINAL ANSWER

2603.88853877871 ≈ 2603.889 Square Meter <-- Total Surface Area of Pentagonal Hexecontahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » CatalanSolids » Pentagonal Hexecontahedron » Surface Area of Pentagonal Hexecontahedron » Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< 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 Insphere Radius Formula

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 Insphere Radius?

Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius calculator uses 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) to calculate the Total Surface Area of Pentagonal Hexecontahedron, Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius formula is defined as the amount or quantity of two-dimensional space covered by the surface of the Pentagonal Hexecontahedron, calculated using insphere radius 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 Insphere Radius using this online calculator? To use this online calculator for Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius, enter Insphere Radius of Pentagonal Hexecontahedron (r_i) and hit the calculate button. Here is how the Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius calculation can be explained with given input values -> 2603.889 = 30*((14*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).

FAQ

What is Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius?

Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius formula is defined as the amount or quantity of two-dimensional space covered by the surface of the Pentagonal Hexecontahedron, calculated using insphere radius of the Pentagonal Hexecontahedron and is represented as TSA = 30*((r_i*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) or 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). Insphere Radius of Pentagonal Hexecontahedron is the radius of the sphere that is contained by the Pentagonal Hexecontahedron in such a way that all the faces just touch the sphere.

How to calculate Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius?

Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius formula is defined as the amount or quantity of two-dimensional space covered by the surface of the Pentagonal Hexecontahedron, calculated using insphere radius of the Pentagonal Hexecontahedron is calculated using 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). To calculate Total Surface Area of Pentagonal Hexecontahedron given Insphere Radius, you need Insphere Radius of Pentagonal Hexecontahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius 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 Insphere Radius 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*((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 = 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*((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)

Home

FREE PDFs

🔍 Search