Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius Calculator

✖Insphere Radius of Pentagonal Icositetrahedron is the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere.ⓘ Insphere Radius of Pentagonal Icositetrahedron [r_i]

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✖SA:V of Pentagonal Icositetrahedron is what part of or fraction of the total volume of Pentagonal Icositetrahedron is the total surface area.ⓘ Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius [R_A/V]

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Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/((2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*Insphere Radius of Pentagonal Icositetrahedron)*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37))))
R_A/V = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/((2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*r_i)*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37))))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[Tribonacci_C] - Tribonacci constant Value Taken As 1.839286755214161

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

SA:V of Pentagonal Icositetrahedron - (Measured in 1 per Meter) - SA:V of Pentagonal Icositetrahedron is what part of or fraction of the total volume of Pentagonal Icositetrahedron is the total surface area.
Insphere Radius of Pentagonal Icositetrahedron - (Measured in Meter) - Insphere Radius of Pentagonal Icositetrahedron is the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Pentagonal Icositetrahedron: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/((2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*r_i)*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))) --> (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/((2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*12)*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37))))

Evaluating ... ...

R_A/V = 0.250000000000002

STEP 3: Convert Result to Output's Unit

0.250000000000002 1 per Meter --> No Conversion Required

FINAL ANSWER

0.250000000000002 ≈ 0.25 1 per Meter <-- SA:V of Pentagonal Icositetrahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< Surface to Volume Ratio of Pentagonal Icositetrahedron Calculators

Surface to Volume Ratio of Pentagonal Icositetrahedron given Total Surface Area

LaTeX Go SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/((sqrt(Total Surface Area of Pentagonal Icositetrahedron/3)*(((4*[Tribonacci_C])-3)/(22*((5*[Tribonacci_C])-1)))^(1/4))*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37))))

Surface to Volume Ratio of Pentagonal Icositetrahedron given Long Edge

LaTeX Go SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(((2*Long Edge of Pentagonal Icositetrahedron)/sqrt([Tribonacci_C]+1))*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37))))

Surface to Volume Ratio of Pentagonal Icositetrahedron given Short Edge

LaTeX Go SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(sqrt([Tribonacci_C]+1)*Short Edge of Pentagonal Icositetrahedron*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37))))

Surface to Volume Ratio of Pentagonal Icositetrahedron

LaTeX Go SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(Snub Cube Edge of Pentagonal Icositetrahedron*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37))))

Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius Formula

LaTeX Go

What is Pentagonal Icositetrahedron?

The Pentagonal Icositetrahedron can be constructed from a snub cube. Its faces are axial-symmetric pentagons with the top angle acos(2-t)=80.7517°. Of this polyhedron, there are two forms that are mirror images of each other, but otherwise identical. It has 24 faces, 60 edges, and 38 vertices.

How to Calculate Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius?

Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius calculator uses SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/((2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*Insphere Radius of Pentagonal Icositetrahedron)*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))) to calculate the SA:V of Pentagonal Icositetrahedron, Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius formula is defined as what part of or fraction of total volume of Pentagonal Icositetrahedron is the total surface area, calculated using insphere radius of Pentagonal Icositetrahedron. SA:V of Pentagonal Icositetrahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius, enter Insphere Radius of Pentagonal Icositetrahedron (r_i) and hit the calculate button. Here is how the Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius calculation can be explained with given input values -> 0.25 = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/((2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*12)*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))).

FAQ

What is Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius?

Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius formula is defined as what part of or fraction of total volume of Pentagonal Icositetrahedron is the total surface area, calculated using insphere radius of Pentagonal Icositetrahedron and is represented as R_A/V = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/((2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*r_i)*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))) or SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/((2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*Insphere Radius of Pentagonal Icositetrahedron)*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))). Insphere Radius of Pentagonal Icositetrahedron is the radius of the sphere that the Pentagonal Icositetrahedron contains in such a way that all the faces touch the sphere.

How to calculate Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius?

Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius formula is defined as what part of or fraction of total volume of Pentagonal Icositetrahedron is the total surface area, calculated using insphere radius of Pentagonal Icositetrahedron is calculated using SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/((2*sqrt((2-[Tribonacci_C])*(3-[Tribonacci_C]))*Insphere Radius of Pentagonal Icositetrahedron)*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37)))). To calculate Surface to Volume Ratio of Pentagonal Icositetrahedron given Insphere Radius, you need Insphere Radius of Pentagonal Icositetrahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Pentagonal Icositetrahedron 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 SA:V of Pentagonal Icositetrahedron?

In this formula, SA:V of Pentagonal Icositetrahedron uses Insphere Radius of Pentagonal Icositetrahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(Snub Cube Edge of Pentagonal Icositetrahedron*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37))))
SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(sqrt([Tribonacci_C]+1)*Short Edge of Pentagonal Icositetrahedron*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37))))
SA:V of Pentagonal Icositetrahedron = (3*sqrt((22*(5*[Tribonacci_C]-1))/((4*[Tribonacci_C])-3)))/(((2*Long Edge of Pentagonal Icositetrahedron)/sqrt([Tribonacci_C]+1))*sqrt((11*([Tribonacci_C]-4))/(2*((20*[Tribonacci_C])-37))))

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