Volume of Star Pyramid given Pentagonal Edge Length of Base Calculator

✖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 [l_e(Pentagon)]			+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%

✖Volume of Star Pyramid is the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid.ⓘ Volume of Star Pyramid given Pentagonal Edge Length of Base [V]

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Formula

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Volume of Star Pyramid given Pentagonal Edge Length of Base

Formula

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

Example

`"207.8564m³"=sqrt(5*(5-(2*sqrt(5))))*(("4m"*"[phi]"^2)^2)/6*"7m"`

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Volume of Star Pyramid given Pentagonal Edge Length of Base Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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

Pentagonal Edge Length of Base of Star Pyramid: 4 Meter --> 4 Meter No Conversion Required
Height of Star Pyramid: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = sqrt(5*(5-(2*sqrt(5))))*((l_e(Pentagon)*[phi]^2)^2)/6*h --> sqrt(5*(5-(2*sqrt(5))))*((4*[phi]^2)^2)/6*7

Evaluating ... ...

V = 207.8563880235

STEP 3: Convert Result to Output's Unit

207.8563880235 Cubic Meter --> No Conversion Required

FINAL ANSWER

207.8563880235 ≈ 207.8564 Cubic Meter <-- Volume of Star Pyramid

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Star Pyramid » Volume and Surface to Volume Ratio of Star Pyramid » Volume of Star Pyramid given Pentagonal Edge Length of Base

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< 5 Volume and Surface to Volume Ratio of Star Pyramid Calculators

Surface to Volume Ratio of Star Pyramid

Go Surface to Volume Ratio of Star Pyramid = ((sqrt(5*(5-(2*sqrt(5))))*(Chord Length of Star Pyramid^2)/2)+ (10*sqrt(((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)*((Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid-Edge Length of Base of Star Pyramid)/2)*((Edge Length of Base of Star Pyramid-Lateral Edge Length of Star Pyramid+Ridge Length of Star Pyramid)/2)* ((Edge Length of Base of Star Pyramid+Lateral Edge Length of Star Pyramid-Ridge Length of Star Pyramid)/2))))/(sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2/6*Height of Star Pyramid)

Volume of Star Pyramid given Lateral Edge Length

Go Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2/6*sqrt(Lateral Edge Length of Star Pyramid^2-(Chord Length of Star Pyramid^2/100*(50+(10*sqrt(5)))))

Volume of Star Pyramid given Edge Length of Base

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

Volume of Star Pyramid given Pentagonal Edge Length of Base

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

Volume of Star Pyramid

Go Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2/6*Height of Star Pyramid

Volume of Star Pyramid given Pentagonal Edge Length of Base Formula

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

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 Volume of Star Pyramid given Pentagonal Edge Length of Base?

Volume of Star Pyramid given Pentagonal Edge Length of Base calculator uses Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*((Pentagonal Edge Length of Base of Star Pyramid*[phi]^2)^2)/6*Height of Star Pyramid to calculate the Volume of Star Pyramid, Volume of Star Pyramid given Pentagonal Edge Length of Base formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid and is calculated using the pentagonal edge length of base, and height of the Star Pyramid. Volume of Star Pyramid is denoted by V symbol.

How to calculate Volume of Star Pyramid given Pentagonal Edge Length of Base using this online calculator? To use this online calculator for Volume of Star Pyramid given Pentagonal Edge Length of Base, enter Pentagonal Edge Length of Base of Star Pyramid (l_e(Pentagon)) & Height of Star Pyramid (h) and hit the calculate button. Here is how the Volume of Star Pyramid given Pentagonal Edge Length of Base calculation can be explained with given input values -> 207.8564 = sqrt(5*(5-(2*sqrt(5))))*((4*[phi]^2)^2)/6*7.

FAQ

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

Volume of Star Pyramid given Pentagonal Edge Length of Base formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid and is calculated using the pentagonal edge length of base, and height of the Star Pyramid and is represented as V = sqrt(5*(5-(2*sqrt(5))))*((l_e(Pentagon)*[phi]^2)^2)/6*h or Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*((Pentagonal Edge Length of Base of Star Pyramid*[phi]^2)^2)/6*Height of Star Pyramid. 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 & 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 Volume of Star Pyramid given Pentagonal Edge Length of Base?

Volume of Star Pyramid given Pentagonal Edge Length of Base formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid and is calculated using the pentagonal edge length of base, and height of the Star Pyramid is calculated using Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*((Pentagonal Edge Length of Base of Star Pyramid*[phi]^2)^2)/6*Height of Star Pyramid. To calculate Volume of Star Pyramid given Pentagonal Edge Length of Base, you need Pentagonal Edge Length of Base of Star Pyramid (l_e(Pentagon)) & Height of Star Pyramid (h). With our tool, you need to enter the respective value for Pentagonal Edge Length of Base 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 Volume of Star Pyramid?

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

Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2/6*Height of Star Pyramid
Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*((Edge Length of Base of Star Pyramid*[phi])^2)/6*Height of Star Pyramid
Volume of Star Pyramid = sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2/6*sqrt(Lateral Edge Length of Star Pyramid^2-(Chord Length of Star Pyramid^2/100*(50+(10*sqrt(5)))))

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