Total Surface Area of Truncated Icosahedron given Circumsphere Radius Calculator

✖Circumsphere Radius of Truncated Icosahedron is the radius of the sphere that contains the Truncated Icosahedron in such a way that all the vertices are lying on the sphere.ⓘ Circumsphere Radius of Truncated Icosahedron [r_c]

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✖Total Surface Area of Truncated Icosahedron is the total quantity of plane enclosed by the entire surface of the Truncated Icosahedron.ⓘ Total Surface Area of Truncated Icosahedron given Circumsphere Radius [TSA]

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Total Surface Area of Truncated Icosahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
TSA = 3*((4*r_c)/(sqrt(58+(18*sqrt(5)))))^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.
Circumsphere Radius of Truncated Icosahedron - (Measured in Meter) - Circumsphere Radius of Truncated Icosahedron is the radius of the sphere that contains the Truncated Icosahedron in such a way that all the vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Truncated Icosahedron: 25 Meter --> 25 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 3*((4*r_c)/(sqrt(58+(18*sqrt(5)))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))) --> 3*((4*25)/(sqrt(58+(18*sqrt(5)))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))

Evaluating ... ...

TSA = 7390.10959856906

STEP 3: Convert Result to Output's Unit

7390.10959856906 Square Meter --> No Conversion Required

FINAL ANSWER

7390.10959856906 ≈ 7390.11 Square Meter <-- Total Surface Area of Truncated Icosahedron

(Calculation completed in 00.020 seconds)

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< Total Surface Area of Truncated Icosahedron Calculators

Total Surface Area of Truncated Icosahedron given Circumsphere Radius

LaTeX 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 Volume

LaTeX 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

LaTeX 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

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

Total Surface Area of Truncated Icosahedron given Circumsphere Radius Formula

LaTeX Go

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 given Circumsphere Radius?

Total Surface Area of Truncated Icosahedron given Circumsphere Radius calculator uses 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)))) to calculate the Total Surface Area of Truncated Icosahedron, Total Surface Area of Truncated Icosahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Icosahedron, and calculated using the circumsphere radius of the Truncated Icosahedron. Total Surface Area of Truncated Icosahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Truncated Icosahedron given Circumsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Truncated Icosahedron given Circumsphere Radius, enter Circumsphere Radius of Truncated Icosahedron (r_c) and hit the calculate button. Here is how the Total Surface Area of Truncated Icosahedron given Circumsphere Radius calculation can be explained with given input values -> 7390.11 = 3*((4*25)/(sqrt(58+(18*sqrt(5)))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))).

FAQ

What is Total Surface Area of Truncated Icosahedron given Circumsphere Radius?

Total Surface Area of Truncated Icosahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Icosahedron, and calculated using the circumsphere radius of the Truncated Icosahedron and is represented as TSA = 3*((4*r_c)/(sqrt(58+(18*sqrt(5)))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))) or 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)))). Circumsphere Radius of Truncated Icosahedron is the radius of the sphere that contains the Truncated Icosahedron in such a way that all the vertices are lying on the sphere.

How to calculate Total Surface Area of Truncated Icosahedron given Circumsphere Radius?

Total Surface Area of Truncated Icosahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Icosahedron, and calculated using the circumsphere radius of the Truncated Icosahedron is calculated using 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)))). To calculate Total Surface Area of Truncated Icosahedron given Circumsphere Radius, you need Circumsphere Radius of Truncated Icosahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius 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 Circumsphere Radius of Truncated Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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