Surface to Volume Ratio of Star Pyramid 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%
✖Edge Length of Base of Star Pyramid is the length of the line joining any two adjacent vertices of the pentagrammic base of the Star Pyramid.ⓘ Edge Length of Base of Star Pyramid [l_e(Base)]			+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%
✖Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex of the Star Pyramid.ⓘ Ridge Length of Star Pyramid [l_e(Ridge)]			+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%

✖Surface to Volume Ratio of Star Pyramid is the numerical ratio of the total surface area of the Star Pyramid to the volume of the Star Pyramid.ⓘ Surface to Volume Ratio of Star Pyramid [R_A/V]

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Formula

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Surface to Volume Ratio of Star Pyramid

Formula

`"R"_{"A/V"} = ((sqrt(5*(5-(2*sqrt(5))))*("l"_{"c"}^2)/2)+ (10*sqrt((("l"_{"e(Base)"}+"l"_{"e(Lateral)"}+"l"_{"e(Ridge)"})/2)*(("l"_{"e(Lateral)"}+"l"_{"e(Ridge)"}-"l"_{"e(Base)"})/2)*(("l"_{"e(Base)"}-"l"_{"e(Lateral)"}+"l"_{"e(Ridge)"})/2)* (("l"_{"e(Base)"}+"l"_{"e(Lateral)"}-"l"_{"e(Ridge)"})/2))))/(sqrt(5*(5-(2*sqrt(5))))*"l"_{"c"}^2/6*"h")`

Example

`"1.664151m⁻¹"=((sqrt(5*(5-(2*sqrt(5))))*(("10m")^2)/2)+ (10*sqrt((("6m"+"11m"+"8m")/2)*(("11m"+"8m"-"6m")/2)*(("6m"-"11m"+"8m")/2)* (("6m"+"11m"-"8m")/2))))/(sqrt(5*(5-(2*sqrt(5))))*("10m")^2/6*"7m")`

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Surface to Volume Ratio of Star Pyramid Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
R_A/V = ((sqrt(5*(5-(2*sqrt(5))))*(l_c^2)/2)+ (10*sqrt(((l_e(Base)+l_e(Lateral)+l_e(Ridge))/2)*((l_e(Lateral)+l_e(Ridge)-l_e(Base))/2)*((l_e(Base)-l_e(Lateral)+l_e(Ridge))/2)* ((l_e(Base)+l_e(Lateral)-l_e(Ridge))/2))))/(sqrt(5*(5-(2*sqrt(5))))*l_c^2/6*h)
This formula uses 1 Functions, 6 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 Star Pyramid - (Measured in 1 per Meter) - Surface to Volume Ratio of Star Pyramid is the numerical ratio of the total surface area of the Star Pyramid to the volume 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.
Edge Length of Base of Star Pyramid - (Measured in Meter) - Edge Length of Base of Star Pyramid is the length of the line joining any two adjacent vertices of the pentagrammic 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.
Ridge Length of Star Pyramid - (Measured in Meter) - Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex 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

Chord Length of Star Pyramid: 10 Meter --> 10 Meter No Conversion Required
Edge Length of Base of Star Pyramid: 6 Meter --> 6 Meter No Conversion Required
Lateral Edge Length of Star Pyramid: 11 Meter --> 11 Meter No Conversion Required
Ridge Length of Star Pyramid: 8 Meter --> 8 Meter No Conversion Required
Height of Star Pyramid: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = ((sqrt(5*(5-(2*sqrt(5))))*(l_c^2)/2)+ (10*sqrt(((l_e(Base)+l_e(Lateral)+l_e(Ridge))/2)*((l_e(Lateral)+l_e(Ridge)-l_e(Base))/2)*((l_e(Base)-l_e(Lateral)+l_e(Ridge))/2)* ((l_e(Base)+l_e(Lateral)-l_e(Ridge))/2))))/(sqrt(5*(5-(2*sqrt(5))))*l_c^2/6*h) --> ((sqrt(5*(5-(2*sqrt(5))))*(10^2)/2)+ (10*sqrt(((6+11+8)/2)*((11+8-6)/2)*((6-11+8)/2)* ((6+11-8)/2))))/(sqrt(5*(5-(2*sqrt(5))))*10^2/6*7)

Evaluating ... ...

R_A/V = 1.66415105545906

STEP 3: Convert Result to Output's Unit

1.66415105545906 1 per Meter --> No Conversion Required

FINAL ANSWER

1.66415105545906 ≈ 1.664151 1 per Meter <-- Surface to Volume Ratio of Star Pyramid

(Calculation completed in 00.004 seconds)

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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

Surface to Volume Ratio of Star Pyramid 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 Surface to Volume Ratio of Star Pyramid?

Surface to Volume Ratio of Star Pyramid calculator uses 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) to calculate the Surface to Volume Ratio of Star Pyramid, Surface to volume ratio of Star Pyramid formula is defined as the numerical ratio of the total surface area of the Star Pyramid to the volume of the Star Pyramid and is calculated using the point edge, point chord, point length, height and ridge length of the Star Pyramid. Surface to Volume Ratio of Star Pyramid is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Star Pyramid using this online calculator? To use this online calculator for Surface to Volume Ratio of Star Pyramid, enter Chord Length of Star Pyramid (l_c), Edge Length of Base of Star Pyramid (l_e(Base)), Lateral Edge Length of Star Pyramid (l_e(Lateral)), Ridge Length of Star Pyramid (l_e(Ridge)) & Height of Star Pyramid (h) and hit the calculate button. Here is how the Surface to Volume Ratio of Star Pyramid calculation can be explained with given input values -> 1.664151 = ((sqrt(5*(5-(2*sqrt(5))))*(10^2)/2)+ (10*sqrt(((6+11+8)/2)*((11+8-6)/2)*((6-11+8)/2)* ((6+11-8)/2))))/(sqrt(5*(5-(2*sqrt(5))))*10^2/6*7).

FAQ

What is Surface to Volume Ratio of Star Pyramid?

Surface to volume ratio of Star Pyramid formula is defined as the numerical ratio of the total surface area of the Star Pyramid to the volume of the Star Pyramid and is calculated using the point edge, point chord, point length, height and ridge length of the Star Pyramid and is represented as R_A/V = ((sqrt(5*(5-(2*sqrt(5))))*(l_c^2)/2)+ (10*sqrt(((l_e(Base)+l_e(Lateral)+l_e(Ridge))/2)*((l_e(Lateral)+l_e(Ridge)-l_e(Base))/2)*((l_e(Base)-l_e(Lateral)+l_e(Ridge))/2)* ((l_e(Base)+l_e(Lateral)-l_e(Ridge))/2))))/(sqrt(5*(5-(2*sqrt(5))))*l_c^2/6*h) or 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). 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, Edge Length of Base of Star Pyramid is the length of the line joining any two adjacent vertices of the pentagrammic 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, Ridge Length of Star Pyramid is the length of the line joining any inner vertex of base of the Star Pyramid and the apex 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 Surface to Volume Ratio of Star Pyramid?

Surface to volume ratio of Star Pyramid formula is defined as the numerical ratio of the total surface area of the Star Pyramid to the volume of the Star Pyramid and is calculated using the point edge, point chord, point length, height and ridge length of the Star Pyramid is calculated using 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). To calculate Surface to Volume Ratio of Star Pyramid, you need Chord Length of Star Pyramid (l_c), Edge Length of Base of Star Pyramid (l_e(Base)), Lateral Edge Length of Star Pyramid (l_e(Lateral)), Ridge Length of Star Pyramid (l_e(Ridge)) & Height of Star Pyramid (h). With our tool, you need to enter the respective value for Chord Length of Star Pyramid, Edge Length of Base of Star Pyramid, Lateral Edge Length of Star Pyramid, Ridge Length 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.

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