Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height Calculator

✖Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.ⓘ Pyramidal Height of Great Dodecahedron [h_Pyramid]

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✖Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.ⓘ Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height [R_A/V]

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Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*Pyramidal Height of Great Dodecahedron)
R_A/V = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*h_Pyramid)
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

Surface to Volume Ratio of Great Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.
Pyramidal Height of Great Dodecahedron - (Measured in Meter) - Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pyramidal Height of Great Dodecahedron: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*h_Pyramid) --> (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*2)

Evaluating ... ...

R_A/V = 0.777739269455689

STEP 3: Convert Result to Output's Unit

0.777739269455689 1 per Meter --> No Conversion Required

FINAL ANSWER

0.777739269455689 ≈ 0.777739 1 per Meter <-- Surface to Volume Ratio of Great Dodecahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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< Surface to Volume Ratio of Great Dodecahedron Calculators

Surface to Volume Ratio of Great Dodecahedron given Circumsphere Radius

LaTeX Go Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*sqrt(10+(2*sqrt(5)))/(4*Circumsphere Radius of Great Dodecahedron)

Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height

LaTeX Go Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*Pyramidal Height of Great Dodecahedron)

Surface to Volume Ratio of Great Dodecahedron

LaTeX Go Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron)

Surface to Volume Ratio of Great Dodecahedron given Ridge Length

LaTeX Go Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4)*1/(2*Ridge Length of Great Dodecahedron)

Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height Formula

LaTeX Go

What is Great Dodecahedron?

The Great Dodecahedron is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height?

Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height calculator uses Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*Pyramidal Height of Great Dodecahedron) to calculate the Surface to Volume Ratio of Great Dodecahedron, Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height formula is defined as the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron, calculated using its pyramidal height. Surface to Volume Ratio of Great Dodecahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height using this online calculator? To use this online calculator for Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height, enter Pyramidal Height of Great Dodecahedron (h_Pyramid) and hit the calculate button. Here is how the Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height calculation can be explained with given input values -> 0.777739 = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*2).

FAQ

What is Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height?

Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height formula is defined as the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron, calculated using its pyramidal height and is represented as R_A/V = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*h_Pyramid) or Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*Pyramidal Height of Great Dodecahedron). Pyramidal Height of Great Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Great Dodecahedron.

How to calculate Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height?

Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height formula is defined as the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron, calculated using its pyramidal height is calculated using Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*(sqrt(3)*(3-sqrt(5)))/(6*Pyramidal Height of Great Dodecahedron). To calculate Surface to Volume Ratio of Great Dodecahedron given Pyramidal Height, you need Pyramidal Height of Great Dodecahedron (h_Pyramid). With our tool, you need to enter the respective value for Pyramidal Height of Great 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 Surface to Volume Ratio of Great Dodecahedron?

In this formula, Surface to Volume Ratio of Great Dodecahedron uses Pyramidal Height of Great Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Edge Length of Great Dodecahedron)
Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4)*1/(2*Ridge Length of Great Dodecahedron)
Surface to Volume Ratio of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1))*sqrt(10+(2*sqrt(5)))/(4*Circumsphere Radius of Great Dodecahedron)

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