Pentagonal Edge Length of Base of Star Pyramid given Volume Calculator

✖Volume of Star Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid.ⓘ Volume of Star Pyramid [V]			+10% -10%
✖Height of Star Pyramid is the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid.ⓘ Height of Star Pyramid [h]			+10% -10%

✖Pentagonal Edge Length of Base of Star Pyramid is the edge length of the regular pentagon from which the pentagrammic base of the Star Pyramid is constructed.ⓘ Pentagonal Edge Length of Base of Star Pyramid given Volume [l_e(Pentagon)]

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Formula

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Pentagonal Edge Length of Base of Star Pyramid given Volume

Formula

`"l"_{"e(Pentagon)"} = (sqrt((6*"V")/(sqrt(5*(5-(2*sqrt(5))))*"h")))/"[phi]"^2`

Example

`"3.923677m"=(sqrt((6*"200m³")/(sqrt(5*(5-(2*sqrt(5))))*"7m")))/"[phi]"^2`

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Pentagonal Edge Length of Base of Star Pyramid given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pentagonal Edge Length of Base of Star Pyramid = (sqrt((6*Volume of Star Pyramid)/(sqrt(5*(5-(2*sqrt(5))))*Height of Star Pyramid)))/[phi]^2
l_e(Pentagon) = (sqrt((6*V)/(sqrt(5*(5-(2*sqrt(5))))*h)))/[phi]^2
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

[phi] - Golden ratio Value Taken As 1.61803398874989484820458683436563811

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

Pentagonal Edge Length of Base of Star Pyramid - (Measured in Meter) - Pentagonal Edge Length of Base of Star Pyramid is the edge length of the regular pentagon from which the pentagrammic base of the Star Pyramid is constructed.
Volume of Star Pyramid - (Measured in Cubic Meter) - Volume of Star Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid.
Height of Star Pyramid - (Measured in Meter) - Height of Star Pyramid is the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid.

STEP 1: Convert Input(s) to Base Unit

Volume of Star Pyramid: 200 Cubic Meter --> 200 Cubic Meter No Conversion Required
Height of Star Pyramid: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e(Pentagon) = (sqrt((6*V)/(sqrt(5*(5-(2*sqrt(5))))*h)))/[phi]^2 --> (sqrt((6*200)/(sqrt(5*(5-(2*sqrt(5))))*7)))/[phi]^2

Evaluating ... ...

l_e(Pentagon) = 3.92367747289454

STEP 3: Convert Result to Output's Unit

3.92367747289454 Meter --> No Conversion Required

FINAL ANSWER

3.92367747289454 ≈ 3.923677 Meter <-- Pentagonal Edge Length of Base of Star Pyramid

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< 4 Pentagonal Edge Length of Star Pyramid Calculators

Pentagonal Edge Length of Base of Star Pyramid given Volume

Go Pentagonal Edge Length of Base of Star Pyramid = (sqrt((6*Volume of Star Pyramid)/(sqrt(5*(5-(2*sqrt(5))))*Height of Star Pyramid)))/[phi]^2

Pentagonal Edge Length of Base of Star Pyramid given Ridge Length

Go Pentagonal Edge Length of Base of Star Pyramid = sqrt(((Ridge Length of Star Pyramid^2-Height of Star Pyramid^2)*100)/(50+(10*sqrt(5))))

Pentagonal Edge Length of Base of Star Pyramid

Go Pentagonal Edge Length of Base of Star Pyramid = Edge Length of Base of Star Pyramid/([phi])

Pentagonal Edge Length of Base of Star Pyramid given Chord Length

Go Pentagonal Edge Length of Base of Star Pyramid = Chord Length of Star Pyramid/[phi]^2

Pentagonal Edge Length of Base of Star Pyramid given Volume Formula

What is a Star Pyramid?

A Star Pyramid is based on a regular pentagram and is concave. It is a pyramid with a pentagrammic base. It has 11 faces which include a pentagram base surface and 10 triangular surfaces. Also, It has 20 edges and 6 vertices.

How to Calculate Pentagonal Edge Length of Base of Star Pyramid given Volume?

Pentagonal Edge Length of Base of Star Pyramid given Volume calculator uses Pentagonal Edge Length of Base of Star Pyramid = (sqrt((6*Volume of Star Pyramid)/(sqrt(5*(5-(2*sqrt(5))))*Height of Star Pyramid)))/[phi]^2 to calculate the Pentagonal Edge Length of Base of Star Pyramid, Pentagonal Edge Length of Base of Star Pyramid given Volume formula is defined as the edge length of the regular pentagon from which the pentagrammic base of the Star Pyramid is constructed and is calculated using the volume and height of the Star Pyramid. Pentagonal Edge Length of Base of Star Pyramid is denoted by l_e(Pentagon) symbol.

How to calculate Pentagonal Edge Length of Base of Star Pyramid given Volume using this online calculator? To use this online calculator for Pentagonal Edge Length of Base of Star Pyramid given Volume, enter Volume of Star Pyramid (V) & Height of Star Pyramid (h) and hit the calculate button. Here is how the Pentagonal Edge Length of Base of Star Pyramid given Volume calculation can be explained with given input values -> 3.923677 = (sqrt((6*200)/(sqrt(5*(5-(2*sqrt(5))))*7)))/[phi]^2.

FAQ

What is Pentagonal Edge Length of Base of Star Pyramid given Volume?

Pentagonal Edge Length of Base of Star Pyramid given Volume formula is defined as the edge length of the regular pentagon from which the pentagrammic base of the Star Pyramid is constructed and is calculated using the volume and height of the Star Pyramid and is represented as l_e(Pentagon) = (sqrt((6*V)/(sqrt(5*(5-(2*sqrt(5))))*h)))/[phi]^2 or Pentagonal Edge Length of Base of Star Pyramid = (sqrt((6*Volume of Star Pyramid)/(sqrt(5*(5-(2*sqrt(5))))*Height of Star Pyramid)))/[phi]^2. Volume of Star Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid & Height of Star Pyramid is the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid.

How to calculate Pentagonal Edge Length of Base of Star Pyramid given Volume?

Pentagonal Edge Length of Base of Star Pyramid given Volume formula is defined as the edge length of the regular pentagon from which the pentagrammic base of the Star Pyramid is constructed and is calculated using the volume and height of the Star Pyramid is calculated using Pentagonal Edge Length of Base of Star Pyramid = (sqrt((6*Volume of Star Pyramid)/(sqrt(5*(5-(2*sqrt(5))))*Height of Star Pyramid)))/[phi]^2. To calculate Pentagonal Edge Length of Base of Star Pyramid given Volume, you need Volume of Star Pyramid (V) & Height of Star Pyramid (h). With our tool, you need to enter the respective value for Volume of Star Pyramid & Height of Star Pyramid 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 Pentagonal Edge Length of Base of Star Pyramid?

In this formula, Pentagonal Edge Length of Base of Star Pyramid uses Volume of Star Pyramid & Height of Star Pyramid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Pentagonal Edge Length of Base of Star Pyramid = Chord Length of Star Pyramid/[phi]^2
Pentagonal Edge Length of Base of Star Pyramid = Edge Length of Base of Star Pyramid/([phi])
Pentagonal Edge Length of Base of Star Pyramid = sqrt(((Ridge Length of Star Pyramid^2-Height of Star Pyramid^2)*100)/(50+(10*sqrt(5))))

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