Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Calculator

✖SA:V of Pentagonal Hexecontahedron is what part of or fraction of total volume of Pentagonal Hexecontahedron is the total surface area.ⓘ SA:V of Pentagonal Hexecontahedron [AV]

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✖Short Edge of Pentagonal Hexecontahedron is the length of the shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron.ⓘ Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio [l_e(Short)]

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Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Edge of Pentagonal Hexecontahedron = (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)))
l_e(Short) = (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(AV*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)))
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

Short Edge of Pentagonal Hexecontahedron - (Measured in Meter) - Short Edge of Pentagonal Hexecontahedron is the length of the shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron.
SA:V of Pentagonal Hexecontahedron - (Measured in 1 per Meter) - SA:V of Pentagonal Hexecontahedron is what part of or fraction of total volume of Pentagonal Hexecontahedron is the total surface area.

STEP 1: Convert Input(s) to Base Unit

SA:V of Pentagonal Hexecontahedron: 0.2 1 per Meter --> 0.2 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e(Short) = (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(AV*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))) --> (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(0.2*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756)))

Evaluating ... ...

l_e(Short) = 4.28629490463292

STEP 3: Convert Result to Output's Unit

4.28629490463292 Meter --> No Conversion Required

FINAL ANSWER

4.28629490463292 ≈ 4.286295 Meter <-- Short Edge of Pentagonal Hexecontahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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< Short Edge of Pentagonal Hexecontahedron Calculators

Short Edge of Pentagonal Hexecontahedron given Long Edge

LaTeX Go Short Edge of Pentagonal Hexecontahedron = (31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756)))

Short Edge of Pentagonal Hexecontahedron given Total Surface Area

LaTeX Go Short Edge of Pentagonal Hexecontahedron = sqrt((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))

Short Edge of Pentagonal Hexecontahedron given Volume

LaTeX Go Short Edge of Pentagonal Hexecontahedron = ((Volume of Pentagonal Hexecontahedron*(1-2*0.4715756^2)*sqrt(1-2*0.4715756))/(5*(1+0.4715756)*(2+3*0.4715756)))^(1/3)

Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge

LaTeX Go Short Edge of Pentagonal Hexecontahedron = Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))

Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio Formula

LaTeX Go

What is Pentagonal Hexecontahedron?

In geometry, a Pentagonal Hexecontahedron is a Catalan solid, dual of the snub dodecahedron. It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. It has 60 faces, 150 edges, 92 vertices. It is the Catalan solid with the most vertices. Among the Catalan and Archimedean solids, it has the second largest number of vertices, after the truncated icosidodecahedron, which has 120 vertices.

How to Calculate Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio?

Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio calculator uses Short Edge of Pentagonal Hexecontahedron = (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))) to calculate the Short Edge of Pentagonal Hexecontahedron, Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio formula is defined as the length of shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron, calculated using surface to volume ratio of Pentagonal Hexecontahedron. Short Edge of Pentagonal Hexecontahedron is denoted by l_e(Short) symbol.

How to calculate Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio, enter SA:V of Pentagonal Hexecontahedron (AV) and hit the calculate button. Here is how the Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio calculation can be explained with given input values -> 4.286295 = (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(0.2*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))).

FAQ

What is Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio?

Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio formula is defined as the length of shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron, calculated using surface to volume ratio of Pentagonal Hexecontahedron and is represented as l_e(Short) = (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(AV*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))) or Short Edge of Pentagonal Hexecontahedron = (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))). SA:V of Pentagonal Hexecontahedron is what part of or fraction of total volume of Pentagonal Hexecontahedron is the total surface area.

How to calculate Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio?

Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio formula is defined as the length of shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron, calculated using surface to volume ratio of Pentagonal Hexecontahedron is calculated using Short Edge of Pentagonal Hexecontahedron = (6*(2+3*0.4715756)*sqrt(1-0.4715756^2)/(1-2*0.4715756^2))/(SA:V of Pentagonal Hexecontahedron*((1+0.4715756)*(2+3*0.4715756))/((1-2*0.4715756^2)*sqrt(1-2*0.4715756))). To calculate Short Edge of Pentagonal Hexecontahedron given Surface to Volume Ratio, you need SA:V of Pentagonal Hexecontahedron (AV). With our tool, you need to enter the respective value for SA:V of Pentagonal Hexecontahedron 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 Short Edge of Pentagonal Hexecontahedron?

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

Short Edge of Pentagonal Hexecontahedron = (31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756)))
Short Edge of Pentagonal Hexecontahedron = Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))
Short Edge of Pentagonal Hexecontahedron = sqrt((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))

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