Total Surface Area of Pentakis Dodecahedron given Midsphere Radius Calculator

✖Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Pentakis Dodecahedron [r_m]

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✖Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron.ⓘ Total Surface Area of Pentakis Dodecahedron given Midsphere Radius [TSA]

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Total Surface Area of Pentakis Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))^2)
TSA = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*r_m)/(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 Pentakis Dodecahedron - (Measured in Square Meter) - Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron.
Midsphere Radius of Pentakis Dodecahedron - (Measured in Meter) - Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Pentakis Dodecahedron: 13 Meter --> 13 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*r_m)/(3+sqrt(5)))^2) --> (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*13)/(3+sqrt(5)))^2)

Evaluating ... ...

TSA = 2167.9672795908

STEP 3: Convert Result to Output's Unit

2167.9672795908 Square Meter --> No Conversion Required

FINAL ANSWER

2167.9672795908 ≈ 2167.967 Square Meter <-- Total Surface Area of Pentakis Dodecahedron

(Calculation completed in 00.004 seconds)

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< Surface Area of Pentakis Dodecahedron Calculators

Total Surface Area of Pentakis Dodecahedron given Volume

LaTeX Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(2/3))

Total Surface Area of Pentakis Dodecahedron given Midsphere Radius

LaTeX Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))^2)

Total Surface Area of Pentakis Dodecahedron given Leg Length

LaTeX Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^2)

Total Surface Area of Pentakis Dodecahedron

LaTeX Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(Base Length of Pentakis Dodecahedron^2)*(sqrt(413+(162*sqrt(5))))

Total Surface Area of Pentakis Dodecahedron given Midsphere Radius Formula

LaTeX Go

What is Pentakis Dodecahedron?

A Pentakis Dodecahedron is a polyhedron with isosceles triangle faces. Five of these are attached as a pyramid on each face of a dodecahedron.
It has 60 faces, 90 edges, 32 vertices.

How to Calculate Total Surface Area of Pentakis Dodecahedron given Midsphere Radius?

Total Surface Area of Pentakis Dodecahedron given Midsphere Radius calculator uses Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))^2) to calculate the Total Surface Area of Pentakis Dodecahedron, Total Surface Area of Pentakis Dodecahedron given Midsphere Radius formula is defined as the amount or quantity of two-dimensional space covered on the surface of the Pentakis Dodecahedron, calculated using midsphere radius of Pentakis Dodecahedron. Total Surface Area of Pentakis Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Pentakis Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Total Surface Area of Pentakis Dodecahedron given Midsphere Radius, enter Midsphere Radius of Pentakis Dodecahedron (r_m) and hit the calculate button. Here is how the Total Surface Area of Pentakis Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 2167.967 = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*13)/(3+sqrt(5)))^2).

FAQ

What is Total Surface Area of Pentakis Dodecahedron given Midsphere Radius?

Total Surface Area of Pentakis Dodecahedron given Midsphere Radius formula is defined as the amount or quantity of two-dimensional space covered on the surface of the Pentakis Dodecahedron, calculated using midsphere radius of Pentakis Dodecahedron and is represented as TSA = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*r_m)/(3+sqrt(5)))^2) or Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))^2). Midsphere Radius of Pentakis Dodecahedron is the radius of the sphere for which all the edges of the Pentakis Dodecahedron become a tangent line on that sphere.

How to calculate Total Surface Area of Pentakis Dodecahedron given Midsphere Radius?

Total Surface Area of Pentakis Dodecahedron given Midsphere Radius formula is defined as the amount or quantity of two-dimensional space covered on the surface of the Pentakis Dodecahedron, calculated using midsphere radius of Pentakis Dodecahedron is calculated using Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((4*Midsphere Radius of Pentakis Dodecahedron)/(3+sqrt(5)))^2). To calculate Total Surface Area of Pentakis Dodecahedron given Midsphere Radius, you need Midsphere Radius of Pentakis Dodecahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Pentakis 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 Pentakis Dodecahedron?

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

Total Surface Area of Pentakis Dodecahedron = (15/19)*(Base Length of Pentakis Dodecahedron^2)*(sqrt(413+(162*sqrt(5))))
Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^2)
Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(2/3))

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