Total Surface Area of Hexakis Icosahedron given Midsphere Radius Calculator

✖Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Hexakis Icosahedron [r_m]

+10%

-10%

✖Total Surface Area of Hexakis Icosahedron is the amount or quantity of two dimensional space covered by the surface of Hexakis Isocahedron.ⓘ Total Surface Area of Hexakis Icosahedron given Midsphere Radius [TSA]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download 3D Geometry Formula PDF PDF Image

Total Surface Area of Hexakis Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))^2)
TSA = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((8*r_m)/(5+(3*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

Total Surface Area of Hexakis Icosahedron - (Measured in Square Meter) - Total Surface Area of Hexakis Icosahedron is the amount or quantity of two dimensional space covered by the surface of Hexakis Isocahedron.
Midsphere Radius of Hexakis Icosahedron - (Measured in Meter) - Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Hexakis Icosahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((8*r_m)/(5+(3*sqrt(5))))^2) --> (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((8*15)/(5+(3*sqrt(5))))^2)

Evaluating ... ...

TSA = 2901.07024516698

STEP 3: Convert Result to Output's Unit

2901.07024516698 Square Meter --> No Conversion Required

FINAL ANSWER

2901.07024516698 ≈ 2901.07 Square Meter <-- Total Surface Area of Hexakis Icosahedron

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » CatalanSolids » Hexakis Icosahedron » Surface Area of Hexakis Icosahedron » Total Surface Area of Hexakis Icosahedron given Midsphere Radius

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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

Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has verified this Calculator and 1800+ more calculators!

< Surface Area of Hexakis Icosahedron Calculators

Total Surface Area of Hexakis Icosahedron given Truncated Icosidodecahedron Edge

LaTeX Go Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(4/25)*(Truncated Edge of Hexakis Icosahedron^2)*(15*(5-sqrt(5)))

Total Surface Area of Hexakis Icosahedron given Medium Edge

LaTeX Go Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))^2)

Total Surface Area of Hexakis Icosahedron given Short Edge

LaTeX Go Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5))))^2)

Total Surface Area of Hexakis Icosahedron

LaTeX Go Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(Long Edge of Hexakis Icosahedron^2)

Total Surface Area of Hexakis Icosahedron given Midsphere Radius Formula

LaTeX Go

What is Hexakis Icosahedron?

A Hexakis Icosahedron is a polyhedron with identical, but irregular triangle faces. It has thirty vertices with four edges, twenty vertices with six edges and twelve vertices with ten edges.
It has 120 faces, 180 edges, 62 vertices.

How to Calculate Total Surface Area of Hexakis Icosahedron given Midsphere Radius?

Total Surface Area of Hexakis Icosahedron given Midsphere Radius calculator uses Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))^2) to calculate the Total Surface Area of Hexakis Icosahedron, Total Surface Area of Hexakis Icosahedron given Midsphere Radius formula is defined as the amount or quantity of two dimensional space covered by the surface of Hexakis Isocahedron, calculated using midsphere radius of Hexakis Icosahedron. Total Surface Area of Hexakis Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Hexakis Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Hexakis Icosahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Icosahedron (r_m) and hit the calculate button. Here is how the Total Surface Area of Hexakis Icosahedron given Midsphere Radius calculation can be explained with given input values -> 2901.07 = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((8*15)/(5+(3*sqrt(5))))^2).

FAQ

What is Total Surface Area of Hexakis Icosahedron given Midsphere Radius?

Total Surface Area of Hexakis Icosahedron given Midsphere Radius formula is defined as the amount or quantity of two dimensional space covered by the surface of Hexakis Isocahedron, calculated using midsphere radius of Hexakis Icosahedron and is represented as TSA = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((8*r_m)/(5+(3*sqrt(5))))^2) or Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))^2). Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.

How to calculate Total Surface Area of Hexakis Icosahedron given Midsphere Radius?

Total Surface Area of Hexakis Icosahedron given Midsphere Radius formula is defined as the amount or quantity of two dimensional space covered by the surface of Hexakis Isocahedron, calculated using midsphere radius of Hexakis Icosahedron is calculated using Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((8*Midsphere Radius of Hexakis Icosahedron)/(5+(3*sqrt(5))))^2). To calculate Total Surface Area of Hexakis Icosahedron given Midsphere Radius, you need Midsphere Radius of Hexakis Icosahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Hexakis Icosahedron 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 Hexakis Icosahedron?

In this formula, Total Surface Area of Hexakis Icosahedron uses Midsphere Radius of Hexakis Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(Long Edge of Hexakis Icosahedron^2)
Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))^2)
Total Surface Area of Hexakis Icosahedron = (15/44)*(sqrt(10*(417+(107*sqrt(5)))))*(((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5))))^2)

Home

FREE PDFs

🔍 Search