Total Surface Area of Great Stellated Dodecahedron given Circumradius Calculator

✖Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.ⓘ Circumradius of Great Stellated Dodecahedron [r_c]

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

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Formula

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Total Surface Area of Great Stellated Dodecahedron given Circumradius

Formula

`"TSA" = 15*sqrt(5+(2*sqrt(5)))*((4*"r"_{"c"})/(sqrt(3)*(3+sqrt(5))))^2`

Example

`"4750.716m²"=15*sqrt(5+(2*sqrt(5)))*((4*"23m")/(sqrt(3)*(3+sqrt(5))))^2`

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Total Surface Area of Great Stellated Dodecahedron given Circumradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2
TSA = 15*sqrt(5+(2*sqrt(5)))*((4*r_c)/(sqrt(3)*(3+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 Great Stellated Dodecahedron - (Measured in Square Meter) - Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron.
Circumradius of Great Stellated Dodecahedron - (Measured in Meter) - Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumradius of Great Stellated Dodecahedron: 23 Meter --> 23 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 15*sqrt(5+(2*sqrt(5)))*((4*r_c)/(sqrt(3)*(3+sqrt(5))))^2 --> 15*sqrt(5+(2*sqrt(5)))*((4*23)/(sqrt(3)*(3+sqrt(5))))^2

Evaluating ... ...

TSA = 4750.71599221201

STEP 3: Convert Result to Output's Unit

4750.71599221201 Square Meter --> No Conversion Required

FINAL ANSWER

4750.71599221201 ≈ 4750.716 Square Meter <-- Total Surface Area of Great Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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< 7 Surface Area of Great Stellated Dodecahedron Calculators

Total Surface Area of Great Stellated Dodecahedron given Surface to Volume Ratio

Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron))^2

Total Surface Area of Great Stellated Dodecahedron given Pyramidal Height

Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2

Total Surface Area of Great Stellated Dodecahedron given Circumradius

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

Total Surface Area of Great Stellated Dodecahedron given Volume

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

Total Surface Area of Great Stellated Dodecahedron given Ridge Length

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

Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord

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

Total Surface Area of Great Stellated Dodecahedron

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

Total Surface Area of Great Stellated Dodecahedron given Circumradius Formula

What is Great Stellated Dodecahedron?

The Great Stellated Dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {⁵⁄₂,3}. It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.

How to Calculate Total Surface Area of Great Stellated Dodecahedron given Circumradius?

Total Surface Area of Great Stellated Dodecahedron given Circumradius calculator uses Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2 to calculate the Total Surface Area of Great Stellated Dodecahedron, Total Surface Area of Great Stellated Dodecahedron given Circumradius formula is defined as the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron, calculated using its circumradius. Total Surface Area of Great Stellated Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Great Stellated Dodecahedron given Circumradius using this online calculator? To use this online calculator for Total Surface Area of Great Stellated Dodecahedron given Circumradius, enter Circumradius of Great Stellated Dodecahedron (r_c) and hit the calculate button. Here is how the Total Surface Area of Great Stellated Dodecahedron given Circumradius calculation can be explained with given input values -> 4750.716 = 15*sqrt(5+(2*sqrt(5)))*((4*23)/(sqrt(3)*(3+sqrt(5))))^2.

FAQ

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

Total Surface Area of Great Stellated Dodecahedron given Circumradius formula is defined as the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron, calculated using its circumradius and is represented as TSA = 15*sqrt(5+(2*sqrt(5)))*((4*r_c)/(sqrt(3)*(3+sqrt(5))))^2 or Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2. Circumradius of Great Stellated Dodecahedron is the radius of sphere that contains Great Stellated Dodecahedron in such a way that all vertices are lying on the sphere.

How to calculate Total Surface Area of Great Stellated Dodecahedron given Circumradius?

Total Surface Area of Great Stellated Dodecahedron given Circumradius formula is defined as the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron, calculated using its circumradius is calculated using Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2. To calculate Total Surface Area of Great Stellated Dodecahedron given Circumradius, you need Circumradius of Great Stellated Dodecahedron (r_c). With our tool, you need to enter the respective value for Circumradius of Great 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 Great Stellated Dodecahedron?

In this formula, Total Surface Area of Great Stellated Dodecahedron uses Circumradius of Great Stellated Dodecahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*Edge Length of Great Stellated Dodecahedron^2
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5)))^2
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^2
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((6*Pyramidal Height of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Volume of Great Stellated Dodecahedron)/(5*(3+sqrt(5))))^(2/3)
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((15*sqrt(5+(2*sqrt(5))))/(5/4*(3+sqrt(5))*SA:V of Great Stellated Dodecahedron))^2

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