Total Surface Area of Small Stellated Dodecahedron given Circumradius Calculator

✖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.ⓘ Circumradius of Small Stellated Dodecahedron [r_c]

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✖Total Surface Area of Small Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Small Stellated Dodecahedron.ⓘ Total Surface Area of Small Stellated Dodecahedron given Circumradius [TSA]

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Total Surface Area of Small Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^2)
TSA = (15*(sqrt(5+2*sqrt(5))))*(((4*r_c)/(sqrt(50+22*sqrt(5))))^2)
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

Total Surface Area of Small Stellated Dodecahedron - (Measured in Square Meter) - Total Surface Area of Small Stellated Dodecahedron is the total quantity of plane enclosed by the entire 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

TSA = (15*(sqrt(5+2*sqrt(5))))*(((4*r_c)/(sqrt(50+22*sqrt(5))))^2) --> (15*(sqrt(5+2*sqrt(5))))*(((4*25)/(sqrt(50+22*sqrt(5))))^2)

Evaluating ... ...

TSA = 4654.06051300047

STEP 3: Convert Result to Output's Unit

4654.06051300047 Square Meter --> No Conversion Required

FINAL ANSWER

4654.06051300047 ≈ 4654.061 Square Meter <-- Total Surface Area of Small Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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< Surface Area of Small Stellated Dodecahedron Calculators

Total Surface Area of Small Stellated Dodecahedron given Circumradius

LaTeX Go Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^2)

Total Surface Area of Small Stellated Dodecahedron given Ridge Length

LaTeX Go Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*(((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))^2)

Total Surface Area of Small Stellated Dodecahedron given Pentagram Chord

LaTeX Go Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*((Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))^2)

Total Surface Area of Small Stellated Dodecahedron

LaTeX Go Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*((Edge Length of Small Stellated Dodecahedron)^2)

Total Surface Area of Small Stellated Dodecahedron given Circumradius Formula

LaTeX Go

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 Total Surface Area of Small Stellated Dodecahedron given Circumradius?

Total Surface Area of Small Stellated Dodecahedron given Circumradius calculator uses Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^2) to calculate the Total Surface Area of Small Stellated Dodecahedron, Total Surface Area of Small Stellated Dodecahedron given Circumradius formula is defined as the total quantity of plane enclosed by the entire surface of the Small Stellated Dodecahedron, calculated using its circumradius. Total Surface Area of Small Stellated Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Small Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Total Surface Area of Small Stellated Dodecahedron given Circumradius, enter Circumradius of Small Stellated Dodecahedron (r_c) and hit the calculate button. Here is how the Total Surface Area of Small Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 4654.061 = (15*(sqrt(5+2*sqrt(5))))*(((4*25)/(sqrt(50+22*sqrt(5))))^2).

FAQ

What is Total Surface Area of Small Stellated Dodecahedron given Circumradius?

Total Surface Area of Small Stellated Dodecahedron given Circumradius formula is defined as the total quantity of plane enclosed by the entire surface of the Small Stellated Dodecahedron, calculated using its circumradius and is represented as TSA = (15*(sqrt(5+2*sqrt(5))))*(((4*r_c)/(sqrt(50+22*sqrt(5))))^2) or Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^2). 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 Total Surface Area of Small Stellated Dodecahedron given Circumradius?

Total Surface Area of Small Stellated Dodecahedron given Circumradius formula is defined as the total quantity of plane enclosed by the entire surface of the Small Stellated Dodecahedron, calculated using its circumradius is calculated using Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*(((4*Circumradius of Small Stellated Dodecahedron)/(sqrt(50+22*sqrt(5))))^2). To calculate Total Surface Area of Small Stellated Dodecahedron given Circumradius, you need Circumradius of Small Stellated Dodecahedron (r_c). 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 Total Surface Area of Small Stellated Dodecahedron?

In this formula, Total Surface Area of Small Stellated Dodecahedron uses Circumradius of Small Stellated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*((Edge Length of Small Stellated Dodecahedron)^2)
Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*(((2*Ridge Length of Small Stellated Dodecahedron)/(1+sqrt(5)))^2)
Total Surface Area of Small Stellated Dodecahedron = (15*(sqrt(5+2*sqrt(5))))*((Pentagram Chord of Small Stellated Dodecahedron/(2+sqrt(5)))^2)

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