Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.ⓘ Surface to Volume Ratio of Pentakis Dodecahedron [R_A/V]

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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 Surface to Volume Ratio [TSA]

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Formula

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Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio

Formula

`"TSA" = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/("R"_{"A/V"}))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2)`

Example

`"3008.845m²"=(15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/("0.2m⁻¹"))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2)`

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Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2)
TSA = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(R_A/V))^2)*((413+(162*sqrt(5)))/((23+(11*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.
Surface to Volume Ratio of Pentakis Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Pentakis Dodecahedron: 0.2 1 per Meter --> 0.2 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(R_A/V))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2) --> (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(0.2))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2)

Evaluating ... ...

TSA = 3008.84546310995

STEP 3: Convert Result to Output's Unit

3008.84546310995 Square Meter --> No Conversion Required

FINAL ANSWER

3008.84546310995 ≈ 3008.845 Square Meter <-- Total Surface Area of Pentakis Dodecahedron

(Calculation completed in 00.021 seconds)

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< 6 Surface Area of Pentakis Dodecahedron Calculators

Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio

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

Total Surface Area of Pentakis Dodecahedron given Insphere Radius

Go Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2)

Total Surface Area of Pentakis Dodecahedron given Volume

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

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

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

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 Surface to Volume Ratio Formula

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 Surface to Volume Ratio?

Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio calculator uses Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2) to calculate the Total Surface Area of Pentakis Dodecahedron, Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as the amount or quantity of two-dimensional space covered on the surface of the Pentakis Dodecahedron, calculated using surface to volume ratio of Pentakis Dodecahedron. Total Surface Area of Pentakis Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Pentakis Dodecahedron (R_A/V) and hit the calculate button. Here is how the Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 3008.845 = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(0.2))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2).

FAQ

What is Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio?

Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as the amount or quantity of two-dimensional space covered on the surface of the Pentakis Dodecahedron, calculated using surface to volume ratio of Pentakis Dodecahedron and is represented as TSA = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(R_A/V))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2) or Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2). Surface to Volume Ratio of Pentakis Dodecahedron is what part of or fraction of total volume of Pentakis Dodecahedron is the total surface area.

How to calculate Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio?

Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio formula is defined as the amount or quantity of two-dimensional space covered on the surface of the Pentakis Dodecahedron, calculated using surface to volume ratio of Pentakis Dodecahedron is calculated using Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((76/19)/(Surface to Volume Ratio of Pentakis Dodecahedron))^2)*((413+(162*sqrt(5)))/((23+(11*sqrt(5))))^2). To calculate Total Surface Area of Pentakis Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Pentakis Dodecahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio of Pentakis Dodecahedron. We can use 5 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))
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 = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2)

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