Volume of Small Stellated Dodecahedron given Pyramidal Height Calculator

✖Pyramidal Height of Small Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron.ⓘ Pyramidal Height of Small Stellated Dodecahedron [h_Pyramid]

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✖Volume of Small Stellated Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Small Stellated Dodecahedron.ⓘ Volume of Small Stellated Dodecahedron given Pyramidal Height [V]

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Formula

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Volume of Small Stellated Dodecahedron given Pyramidal Height

Formula

`"V" = ((5/4)*(7+3*sqrt(5)))*(((5*"h"_{"Pyramid"})/(sqrt(25+10*sqrt(5))))^3)`

Example

`"18032.58m³"=((5/4)*(7+3*sqrt(5)))*(((5*"14m")/(sqrt(25+10*sqrt(5))))^3)`

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Volume of Small Stellated Dodecahedron given Pyramidal Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))^3)
V = ((5/4)*(7+3*sqrt(5)))*(((5*h_Pyramid)/(sqrt(25+10*sqrt(5))))^3)
This formula uses 1 Functions, 2 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 Small Stellated Dodecahedron - (Measured in Cubic Meter) - Volume of Small Stellated Dodecahedron is the total quantity of three-dimensional space enclosed by the surface of the Small Stellated Dodecahedron.
Pyramidal Height of Small Stellated Dodecahedron - (Measured in Meter) - Pyramidal Height of Small Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pyramidal Height of Small Stellated Dodecahedron: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = ((5/4)*(7+3*sqrt(5)))*(((5*h_Pyramid)/(sqrt(25+10*sqrt(5))))^3) --> ((5/4)*(7+3*sqrt(5)))*(((5*14)/(sqrt(25+10*sqrt(5))))^3)

Evaluating ... ...

V = 18032.5771456863

STEP 3: Convert Result to Output's Unit

18032.5771456863 Cubic Meter --> No Conversion Required

FINAL ANSWER

18032.5771456863 ≈ 18032.58 Cubic Meter <-- Volume of Small Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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< 7 Volume of Small Stellated Dodecahedron Calculators

Volume of Small Stellated Dodecahedron given Surface to Volume Ratio

Go Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron))^3)

Volume of Small Stellated Dodecahedron given Total Surface Area

Go Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*((Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5)))))^(3/2))

Volume of Small Stellated Dodecahedron given Pyramidal Height

Go Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))^3)

Volume of Small Stellated Dodecahedron given Circumradius

Go Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^3)

Volume of Small Stellated Dodecahedron given Ridge Length

Go Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))^3)

Volume of Small Stellated Dodecahedron given Pentagram Chord

Go Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*((Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))^3)

Volume of Small Stellated Dodecahedron

Go Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*((Edge Length of Small Stellated Dodecahedron)^3)

Volume of Small Stellated Dodecahedron given Pyramidal Height Formula

What is Small Stellated Dodecahedron?

The Small Stellated Dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2,5}. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.

How to Calculate Volume of Small Stellated Dodecahedron given Pyramidal Height?

Volume of Small Stellated Dodecahedron given Pyramidal Height calculator uses Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))^3) to calculate the Volume of Small Stellated Dodecahedron, Volume of Small Stellated Dodecahedron given Pyramidal Height formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Small Stellated Dodecahedron, calculated using its pyramidal height. Volume of Small Stellated Dodecahedron is denoted by V symbol.

How to calculate Volume of Small Stellated Dodecahedron given Pyramidal Height using this online calculator? To use this online calculator for Volume of Small Stellated Dodecahedron given Pyramidal Height, enter Pyramidal Height of Small Stellated Dodecahedron (h_Pyramid) and hit the calculate button. Here is how the Volume of Small Stellated Dodecahedron given Pyramidal Height calculation can be explained with given input values -> 18032.58 = ((5/4)*(7+3*sqrt(5)))*(((5*14)/(sqrt(25+10*sqrt(5))))^3).

FAQ

What is Volume of Small Stellated Dodecahedron given Pyramidal Height?

Volume of Small Stellated Dodecahedron given Pyramidal Height formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Small Stellated Dodecahedron, calculated using its pyramidal height and is represented as V = ((5/4)*(7+3*sqrt(5)))*(((5*h_Pyramid)/(sqrt(25+10*sqrt(5))))^3) or Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))^3). Pyramidal Height of Small Stellated Dodecahedron is the height of any of the inwards directed tetrahedral pyramids of the Small Stellated Dodecahedron.

How to calculate Volume of Small Stellated Dodecahedron given Pyramidal Height?

Volume of Small Stellated Dodecahedron given Pyramidal Height formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Small Stellated Dodecahedron, calculated using its pyramidal height is calculated using Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*sqrt(5))))^3). To calculate Volume of Small Stellated Dodecahedron given Pyramidal Height, you need Pyramidal Height of Small Stellated Dodecahedron (h_Pyramid). With our tool, you need to enter the respective value for Pyramidal Height of Small Stellated Dodecahedron 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 Small Stellated Dodecahedron?

In this formula, Volume of Small Stellated Dodecahedron uses Pyramidal Height of Small Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*((Edge Length of Small Stellated Dodecahedron)^3)
Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))^3)
Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*((Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))^3)
Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^3)
Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*((Total Surface Area of Small Stellated Dodecahedron/(15*(sqrt(5+2*sqrt(5)))))^(3/2))
Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((15*(sqrt(5+2*sqrt(5))))/((5/4)*(7+3*sqrt(5))*SA:V of Small Stellated Dodecahedron))^3)

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