Volume of Star Pyramid given Lateral Edge Length Calculator

✖Chord Length of Star Pyramid is the length of the straight line joining two adjacent spike points or outer vertices of the base of the Star Pyramid.ⓘ Chord Length of Star Pyramid [l_c]			+10% -10%
✖Lateral Edge Length of Star Pyramid is the length of the line joining any spike or outer vertex of base of the Star Pyramid and the apex of the Star Pyramid.ⓘ Lateral Edge Length of Star Pyramid [l_e(Lateral)]			+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 Lateral Edge Length [V]

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Formula

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Volume of Star Pyramid given Lateral Edge Length

Formula

`"V" = sqrt(5*(5-(2*sqrt(5))))*"l"_{"c"}^2/6*sqrt("l"_{"e(Lateral)"}^2-("l"_{"c"}^2/100*(50+(10*sqrt(5)))))`

Example

`"188.8376m³"=sqrt(5*(5-(2*sqrt(5))))*("10m")^2/6*sqrt(("11m")^2-(("10m")^2/100*(50+(10*sqrt(5)))))`

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Volume of Star Pyramid given Lateral Edge Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))))
V = sqrt(5*(5-(2*sqrt(5))))*l_c^2/6*sqrt(l_e(Lateral)^2-(l_c^2/100*(50+(10*sqrt(5)))))
This formula uses 1 Functions, 3 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

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.
Chord Length of Star Pyramid - (Measured in Meter) - Chord Length of Star Pyramid is the length of the straight line joining two adjacent spike points or outer vertices of the base of the Star Pyramid.
Lateral Edge Length of Star Pyramid - (Measured in Meter) - Lateral Edge Length of Star Pyramid is the length of the line joining any spike or outer vertex of base of the Star Pyramid and the apex of the Star Pyramid.

STEP 1: Convert Input(s) to Base Unit

Chord Length of Star Pyramid: 10 Meter --> 10 Meter No Conversion Required
Lateral Edge Length of Star Pyramid: 11 Meter --> 11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = sqrt(5*(5-(2*sqrt(5))))*l_c^2/6*sqrt(l_e(Lateral)^2-(l_c^2/100*(50+(10*sqrt(5))))) --> sqrt(5*(5-(2*sqrt(5))))*10^2/6*sqrt(11^2-(10^2/100*(50+(10*sqrt(5)))))

Evaluating ... ...

V = 188.837629842414

STEP 3: Convert Result to Output's Unit

188.837629842414 Cubic Meter --> No Conversion Required

FINAL ANSWER

188.837629842414 ≈ 188.8376 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 Lateral Edge Length

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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 Lateral Edge Length 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 Volume of Star Pyramid given Lateral Edge Length?

Volume of Star Pyramid given Lateral Edge Length calculator uses 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))))) to calculate the Volume of Star Pyramid, Volume of Star Pyramid given Lateral Edge Length formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid and is calculated using the lateral edge length, and chord length of the Star Pyramid. Volume of Star Pyramid is denoted by V symbol.

How to calculate Volume of Star Pyramid given Lateral Edge Length using this online calculator? To use this online calculator for Volume of Star Pyramid given Lateral Edge Length, enter Chord Length of Star Pyramid (l_c) & Lateral Edge Length of Star Pyramid (l_e(Lateral)) and hit the calculate button. Here is how the Volume of Star Pyramid given Lateral Edge Length calculation can be explained with given input values -> 188.8376 = sqrt(5*(5-(2*sqrt(5))))*10^2/6*sqrt(11^2-(10^2/100*(50+(10*sqrt(5))))).

FAQ

What is Volume of Star Pyramid given Lateral Edge Length?

Volume of Star Pyramid given Lateral Edge Length formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid and is calculated using the lateral edge length, and chord length of the Star Pyramid and is represented as V = sqrt(5*(5-(2*sqrt(5))))*l_c^2/6*sqrt(l_e(Lateral)^2-(l_c^2/100*(50+(10*sqrt(5))))) or 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))))). Chord Length of Star Pyramid is the length of the straight line joining two adjacent spike points or outer vertices of the base of the Star Pyramid & Lateral Edge Length of Star Pyramid is the length of the line joining any spike or outer vertex of base of the Star Pyramid and the apex of the Star Pyramid.

How to calculate Volume of Star Pyramid given Lateral Edge Length?

Volume of Star Pyramid given Lateral Edge Length formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Star Pyramid and is calculated using the lateral edge length, and chord length of the Star Pyramid is calculated using 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))))). To calculate Volume of Star Pyramid given Lateral Edge Length, you need Chord Length of Star Pyramid (l_c) & Lateral Edge Length of Star Pyramid (l_e(Lateral)). With our tool, you need to enter the respective value for Chord Length of Star Pyramid & Lateral Edge Length 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 Chord Length of Star Pyramid & Lateral Edge Length 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))))*((Pentagonal Edge Length of Base of Star Pyramid*[phi]^2)^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

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