Total Surface Area of Truncated Dodecahedron given Circumsphere Radius Calculator

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

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

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Total Surface Area of Truncated Dodecahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^2
TSA = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*r_c)/(sqrt(74+(30*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 Truncated Dodecahedron - (Measured in Square Meter) - Total Surface Area of Truncated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Truncated Dodecahedron.
Circumsphere Radius of Truncated Dodecahedron - (Measured in Meter) - Circumsphere Radius of Truncated Dodecahedron is the radius of the sphere that contains the Truncated Dodecahedron 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 Dodecahedron: 30 Meter --> 30 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*r_c)/(sqrt(74+(30*sqrt(5)))))^2 --> 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*30)/(sqrt(74+(30*sqrt(5)))))^2

Evaluating ... ...

TSA = 10307.9524024646

STEP 3: Convert Result to Output's Unit

10307.9524024646 Square Meter --> No Conversion Required

FINAL ANSWER

10307.9524024646 ≈ 10307.95 Square Meter <-- Total Surface Area of Truncated Dodecahedron

(Calculation completed in 00.004 seconds)

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< Total Surface Area of Truncated Dodecahedron Calculators

Total Surface Area of Truncated Dodecahedron given Circumsphere Radius

LaTeX Go Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^2

Total Surface Area of Truncated Dodecahedron given Volume

LaTeX Go Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(2/3)

Total Surface Area of Truncated Dodecahedron given Dodecahedral Edge Length

LaTeX Go Total Surface Area of Truncated Dodecahedron = (sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*Dodecahedral Edge Length of Truncated Dodecahedron^2

Total Surface Area of Truncated Dodecahedron

LaTeX Go Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*Edge Length of Truncated Dodecahedron^2

Total Surface Area of Truncated Dodecahedron given Circumsphere Radius Formula

LaTeX Go

What is a Truncated Dodecahedron?

In geometry, the Truncated Dodecahedron is an Archimedean solid. It has a total of 32 faces - 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. Each vertex is identical in such a way that two decagonal faces and one triangular face join at each vertex. This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles. The Truncated Dodecahedron has five special orthogonal projections, centered, on a vertex, on two types of edges, and two types of faces: hexagonal and pentagonal.

How to Calculate Total Surface Area of Truncated Dodecahedron given Circumsphere Radius?

Total Surface Area of Truncated Dodecahedron given Circumsphere Radius calculator uses Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^2 to calculate the Total Surface Area of Truncated Dodecahedron, Total Surface Area of Truncated Dodecahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Dodecahedron, and calculated using the circumsphere radius of the Truncated Dodecahedron. Total Surface Area of Truncated Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Truncated Dodecahedron given Circumsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Truncated Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Truncated Dodecahedron (r_c) and hit the calculate button. Here is how the Total Surface Area of Truncated Dodecahedron given Circumsphere Radius calculation can be explained with given input values -> 10307.95 = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*30)/(sqrt(74+(30*sqrt(5)))))^2.

FAQ

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

Total Surface Area of Truncated Dodecahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Dodecahedron, and calculated using the circumsphere radius of the Truncated Dodecahedron and is represented as TSA = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*r_c)/(sqrt(74+(30*sqrt(5)))))^2 or Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^2. Circumsphere Radius of Truncated Dodecahedron is the radius of the sphere that contains the Truncated Dodecahedron in such a way that all the vertices are lying on the sphere.

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

Total Surface Area of Truncated Dodecahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Dodecahedron, and calculated using the circumsphere radius of the Truncated Dodecahedron is calculated using Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^2. To calculate Total Surface Area of Truncated Dodecahedron given Circumsphere Radius, you need Circumsphere Radius of Truncated Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of Truncated Dodecahedron 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 Dodecahedron?

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

Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*Edge Length of Truncated Dodecahedron^2
Total Surface Area of Truncated Dodecahedron = (sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*Dodecahedral Edge Length of Truncated Dodecahedron^2
Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(2/3)

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