Total Surface Area of Truncated Icosahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
TSA = 3*le^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
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 Truncated Icosahedron - (Measured in Square Meter) - Total Surface Area of Truncated Icosahedron is the total quantity of plane enclosed by the entire surface of the Truncated Icosahedron.
Edge Length of Truncated Icosahedron - (Measured in Meter) - Edge Length of Truncated Icosahedron is the length of any edge of the Truncated Icosahedron.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Truncated Icosahedron: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = 3*le^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))) --> 3*10^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Evaluating ... ...
TSA = 7260.72530341339
STEP 3: Convert Result to Output's Unit
7260.72530341339 Square Meter --> No Conversion Required
FINAL ANSWER
7260.72530341339 7260.725 Square Meter <-- Total Surface Area of Truncated Icosahedron
(Calculation completed in 00.004 seconds)

Credits

Created by Mona Gladys
St Joseph's College (SJC), Bengaluru
Mona Gladys has created this Calculator and 2000+ more calculators!
Verified by Mridul Sharma
Indian Institute of Information Technology (IIIT), Bhopal
Mridul Sharma has verified this Calculator and 1700+ more calculators!

6 Total Surface Area of Truncated Icosahedron Calculators

Total Surface Area of Truncated Icosahedron given Surface to Volume Ratio
Go Total Surface Area of Truncated Icosahedron = 3*((12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Total Surface Area of Truncated Icosahedron given Circumsphere Radius
Go Total Surface Area of Truncated Icosahedron = 3*((4*Circumsphere Radius of Truncated Icosahedron)/(sqrt(58+(18*sqrt(5)))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Total Surface Area of Truncated Icosahedron given Midsphere Radius
Go Total Surface Area of Truncated Icosahedron = 3*((4*Midsphere Radius of Truncated Icosahedron)/(3*(1+sqrt(5))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Total Surface Area of Truncated Icosahedron given Volume
Go Total Surface Area of Truncated Icosahedron = 3*((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(2/3)*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Total Surface Area of Truncated Icosahedron given Icosahedral Edge Length
Go Total Surface Area of Truncated Icosahedron = (Icosahedral Edge Length of Truncated Icosahedron^2)/3*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Total Surface Area of Truncated Icosahedron
Go Total Surface Area of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))

12 Important Formulas of Truncated Icosahedron Calculators

Volume of Truncated Icosahedron given Total Surface Area
Go Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*(sqrt(Total Surface Area of Truncated Icosahedron/(3*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))))^3
Surface to Volume Ratio of Truncated Icosahedron
Go Surface to Volume Ratio of Truncated Icosahedron = (12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Edge Length of Truncated Icosahedron*(125+(43*sqrt(5))))
Total Surface Area of Truncated Icosahedron given Volume
Go Total Surface Area of Truncated Icosahedron = 3*((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(2/3)*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Total Surface Area of Truncated Icosahedron
Go Total Surface Area of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Edge Length of Truncated Icosahedron given Circumsphere Radius
Go Edge Length of Truncated Icosahedron = (4*Circumsphere Radius of Truncated Icosahedron)/(sqrt(58+(18*sqrt(5))))
Circumsphere Radius of Truncated Icosahedron
Go Circumsphere Radius of Truncated Icosahedron = (sqrt(58+(18*sqrt(5))))/4*Edge Length of Truncated Icosahedron
Midsphere Radius of Truncated Icosahedron given Icosahedral Edge Length
Go Midsphere Radius of Truncated Icosahedron = (1+sqrt(5))/4*Icosahedral Edge Length of Truncated Icosahedron
Edge Length of Truncated Icosahedron given Volume
Go Edge Length of Truncated Icosahedron = ((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(1/3)
Edge Length of Truncated Icosahedron given Midsphere Radius
Go Edge Length of Truncated Icosahedron = (4*Midsphere Radius of Truncated Icosahedron)/(3*(1+sqrt(5)))
Midsphere Radius of Truncated Icosahedron
Go Midsphere Radius of Truncated Icosahedron = (3*(1+sqrt(5)))/4*Edge Length of Truncated Icosahedron
Volume of Truncated Icosahedron
Go Volume of Truncated Icosahedron = (125+(43*sqrt(5)))/4*Edge Length of Truncated Icosahedron^3
Icosahedral Edge Length of Truncated Icosahedron
Go Icosahedral Edge Length of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron

Total Surface Area of Truncated Icosahedron Formula

Total Surface Area of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
TSA = 3*le^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))

What is Truncated Icosahedron and its applications?

In geometry, the Truncated Icosahedron is an Archimedean solid, one of 13 convex isogonal non-prismatic solids whose faces are two or more types of regular polygons. It has a total of 32 faces which include 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges. It is the Goldberg polyhedron GPV(1,1) or {5+,3}1,1, containing pentagonal and hexagonal faces. This geometry is associated with footballs (soccer balls) typically patterned with white hexagons and black pentagons. Geodesic domes such as those whose architecture Buckminster Fuller pioneered are often based on this structure. It also corresponds to the geometry of the fullerene C60 ("buckyball") molecule. It is used in the cell-transitive hyperbolic space-filling tessellation, the bi-truncated order-5 dodecahedral honeycomb.

How to Calculate Total Surface Area of Truncated Icosahedron?

Total Surface Area of Truncated Icosahedron calculator uses Total Surface Area of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))) to calculate the Total Surface Area of Truncated Icosahedron, Total Surface Area of Truncated Icosahedron formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Icosahedron. Total Surface Area of Truncated Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Truncated Icosahedron using this online calculator? To use this online calculator for Total Surface Area of Truncated Icosahedron, enter Edge Length of Truncated Icosahedron (le) and hit the calculate button. Here is how the Total Surface Area of Truncated Icosahedron calculation can be explained with given input values -> 7260.725 = 3*10^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))).

FAQ

What is Total Surface Area of Truncated Icosahedron?
Total Surface Area of Truncated Icosahedron formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Icosahedron and is represented as TSA = 3*le^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))) or Total Surface Area of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))). Edge Length of Truncated Icosahedron is the length of any edge of the Truncated Icosahedron.
How to calculate Total Surface Area of Truncated Icosahedron?
Total Surface Area of Truncated Icosahedron formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Icosahedron is calculated using Total Surface Area of Truncated Icosahedron = 3*Edge Length of Truncated Icosahedron^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))). To calculate Total Surface Area of Truncated Icosahedron, you need Edge Length of Truncated Icosahedron (le). With our tool, you need to enter the respective value for Edge Length of Truncated 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 Truncated Icosahedron?
In this formula, Total Surface Area of Truncated Icosahedron uses Edge Length of Truncated Icosahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Total Surface Area of Truncated Icosahedron = (Icosahedral Edge Length of Truncated Icosahedron^2)/3*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
  • Total Surface Area of Truncated Icosahedron = 3*((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(2/3)*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
  • Total Surface Area of Truncated Icosahedron = 3*((4*Circumsphere Radius of Truncated Icosahedron)/(sqrt(58+(18*sqrt(5)))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
  • Total Surface Area of Truncated Icosahedron = 3*((4*Midsphere Radius of Truncated Icosahedron)/(3*(1+sqrt(5))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
  • Total Surface Area of Truncated Icosahedron = 3*((12*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))))/(Surface to Volume Ratio of Truncated Icosahedron*(125+(43*sqrt(5)))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
  • Total Surface Area of Truncated Icosahedron = 3*((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(2/3)*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!