Volume of Small Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^3)
V = ((5/4)*(7+3*sqrt(5)))*(((4*rc)/(sqrt(50+22*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.
Circumradius of Small Stellated Dodecahedron - (Measured in Meter) - Circumradius of Small Stellated Dodecahedron is the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere.
STEP 1: Convert Input(s) to Base Unit
Circumradius of Small Stellated Dodecahedron: 25 Meter --> 25 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
V = ((5/4)*(7+3*sqrt(5)))*(((4*rc)/(sqrt(50+22*sqrt(5))))^3) --> ((5/4)*(7+3*sqrt(5)))*(((4*25)/(sqrt(50+22*sqrt(5))))^3)
Evaluating ... ...
V = 17344.659464111
STEP 3: Convert Result to Output's Unit
17344.659464111 Cubic Meter --> No Conversion Required
FINAL ANSWER
17344.659464111 17344.66 Cubic Meter <-- Volume of Small Stellated Dodecahedron
(Calculation completed in 00.020 seconds)

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Walchand College of Engineering (WCE), Sangli
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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 Circumradius Formula

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

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 Circumradius?

Volume of Small Stellated Dodecahedron given Circumradius calculator uses Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^3) to calculate the Volume of Small Stellated Dodecahedron, Volume of Small Stellated Dodecahedron given Circumradius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Small Stellated Dodecahedron, calculated using its circumradius. Volume of Small Stellated Dodecahedron is denoted by V symbol.

How to calculate Volume of Small Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Volume of Small Stellated Dodecahedron given Circumradius, enter Circumradius of Small Stellated Dodecahedron (rc) and hit the calculate button. Here is how the Volume of Small Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 17344.66 = ((5/4)*(7+3*sqrt(5)))*(((4*25)/(sqrt(50+22*sqrt(5))))^3).

FAQ

What is Volume of Small Stellated Dodecahedron given Circumradius?
Volume of Small Stellated Dodecahedron given Circumradius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Small Stellated Dodecahedron, calculated using its circumradius and is represented as V = ((5/4)*(7+3*sqrt(5)))*(((4*rc)/(sqrt(50+22*sqrt(5))))^3) or Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^3). Circumradius of Small Stellated Dodecahedron is the radius of sphere that contains the Small Stellated Dodecahedron in such a way that all vertices are lying on sphere.
How to calculate Volume of Small Stellated Dodecahedron given Circumradius?
Volume of Small Stellated Dodecahedron given Circumradius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Small Stellated Dodecahedron, calculated using its circumradius is calculated using Volume of Small Stellated Dodecahedron = ((5/4)*(7+3*sqrt(5)))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^3). To calculate Volume of Small Stellated Dodecahedron given Circumradius, you need Circumradius of Small Stellated Dodecahedron (rc). With our tool, you need to enter the respective value for Circumradius 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 Circumradius 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)))*(((5*Pyramidal Height of Small Stellated Dodecahedron)/(sqrt(25+10*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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