Height 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%
✖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%

✖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 given Volume [h]

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Height of Star Pyramid given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Volume of Star Pyramid: 200 Cubic Meter --> 200 Cubic Meter No Conversion Required
Chord Length of Star Pyramid: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = (6*V)/(sqrt(5*(5-(2*sqrt(5))))*l_c^2) --> (6*200)/(sqrt(5*(5-(2*sqrt(5))))*10^2)

Evaluating ... ...

h = 7.38644048922061

STEP 3: Convert Result to Output's Unit

7.38644048922061 Meter --> No Conversion Required

FINAL ANSWER

7.38644048922061 ≈ 7.38644 Meter <-- Height of Star Pyramid

(Calculation completed in 00.020 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< Height of Star Pyramid Calculators

Height of Star Pyramid given Ridge Length

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

Height of Star Pyramid given Lateral Edge Length

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

Height of Star Pyramid given Volume

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

Height of Star Pyramid given Volume Formula

LaTeX Go

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

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 Height of Star Pyramid given Volume?

Height of Star Pyramid given Volume calculator uses Height of Star Pyramid = (6*Volume of Star Pyramid)/(sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2) to calculate the Height of Star Pyramid, Height of Star Pyramid given Volume formula is defined as the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid and is calculated using the volume and chord length of the Star Pyramid. Height of Star Pyramid is denoted by h symbol.

How to calculate Height of Star Pyramid given Volume using this online calculator? To use this online calculator for Height of Star Pyramid given Volume, enter Volume of Star Pyramid (V) & Chord Length of Star Pyramid (l_c) and hit the calculate button. Here is how the Height of Star Pyramid given Volume calculation can be explained with given input values -> 7.38644 = (6*200)/(sqrt(5*(5-(2*sqrt(5))))*10^2).

FAQ

What is Height of Star Pyramid given Volume?

Height of Star Pyramid given Volume formula is defined as the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid and is calculated using the volume and chord length of the Star Pyramid and is represented as h = (6*V)/(sqrt(5*(5-(2*sqrt(5))))*l_c^2) or Height of Star Pyramid = (6*Volume of Star Pyramid)/(sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2). 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 is the length of the straight line joining two adjacent spike points or outer vertices of the base of the Star Pyramid.

How to calculate Height of Star Pyramid given Volume?

Height of Star Pyramid given Volume formula is defined as the length of the perpendicular from the apex of the Star Pyramid, where the five spikes meet to the base of the Star Pyramid and is calculated using the volume and chord length of the Star Pyramid is calculated using Height of Star Pyramid = (6*Volume of Star Pyramid)/(sqrt(5*(5-(2*sqrt(5))))*Chord Length of Star Pyramid^2). To calculate Height of Star Pyramid given Volume, you need Volume of Star Pyramid (V) & Chord Length of Star Pyramid (l_c). With our tool, you need to enter the respective value for Volume of Star Pyramid & Chord 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 Height of Star Pyramid?

In this formula, Height of Star Pyramid uses Volume of Star Pyramid & Chord Length of Star Pyramid. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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