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Total Surface Area of Great Dodecahedron given Circumsphere Radius Formula

GoTotal Surface Area of Great Dodecahedron Formula

GoTotal Surface Area of Great Dodecahedron given Ridge Length Formula

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Total Surface Area of Great Dodecahedron is the total quantity of plane enclosed on the entire surface of the Great Dodecahedron. Check FAQs

TSA = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

TSA - Total Surface Area of Great Dodecahedron?r_c - Circumsphere Radius of Great Dodecahedron?

Total Surface Area of Great Dodecahedron given Circumsphere Radius Example

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Here is how the Total Surface Area of Great Dodecahedron given Circumsphere Radius equation looks like with Values.

Here is how the Total Surface Area of Great Dodecahedron given Circumsphere Radius equation looks like with Units.

Here is how the Total Surface Area of Great Dodecahedron given Circumsphere Radius equation looks like.

975.9435 = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

975.9435m² = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

975.9435 = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

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Total Surface Area of Great Dodecahedron given Circumsphere Radius Solution

Follow our step by step solution on how to calculate Total Surface Area of Great Dodecahedron given Circumsphere Radius?

FIRST Step Consider the formula

TSA = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Substitute values of Variables

∴

TSA = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Evaluate

∴

TSA = 975.943481207065m²

LAST Step Rounding Answer

∴

TSA = 975.9435m²

Total Surface Area of Great Dodecahedron given Circumsphere Radius Formula Elements

Variables

Functions

Total Surface Area of Great Dodecahedron

Total Surface Area of Great Dodecahedron is the total quantity of plane enclosed on the entire surface of the Great Dodecahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Great Dodecahedron

Circumsphere Radius of Great Dodecahedron

Circumsphere Radius of Great Dodecahedron is the radius of the sphere that contains the Great Dodecahedron in such a way that all the vertices are lying on sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of Great Dodecahedron

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.

Syntax: sqrt(Number)

Other Formulas to find Total Surface Area of Great Dodecahedron

Go Total Surface Area of Great Dodecahedron

TSA = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {l e}^{2}

Go Total Surface Area of Great Dodecahedron given Ridge Length

TSA = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot l Ridge}{\sqrt{5} - 1})}^{2}

Go Total Surface Area of Great Dodecahedron given Pyramidal Height

TSA = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {(\frac{6 \cdot h Pyramid}{\sqrt{3} \cdot (3 - \sqrt{5})})}^{2}

Go Total Surface Area of Great Dodecahedron given Volume

TSA = 15 \cdot \sqrt{5 - (2 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot V}{5 \cdot (\sqrt{5} - 1)})}^{\frac{2}{3}}

How to Evaluate Total Surface Area of Great Dodecahedron given Circumsphere Radius?

Total Surface Area of Great Dodecahedron given Circumsphere Radius evaluator uses Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^2 to evaluate the Total Surface Area of Great Dodecahedron, Total Surface Area of Great Dodecahedron given Circumsphere Radius formula is the total quantity of plane enclosed on the entire surface of the Great Dodecahedron, calculated using its circumsphere radius. Total Surface Area of Great Dodecahedron is denoted by TSA symbol.

How to evaluate Total Surface Area of Great Dodecahedron given Circumsphere Radius using this online evaluator? To use this online evaluator for Total Surface Area of Great Dodecahedron given Circumsphere Radius, enter Circumsphere Radius of Great Dodecahedron (r_c) and hit the calculate button.

FAQs on Total Surface Area of Great Dodecahedron given Circumsphere Radius

What is the formula to find Total Surface Area of Great Dodecahedron given Circumsphere Radius?

The formula of Total Surface Area of Great Dodecahedron given Circumsphere Radius is expressed as Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^2. Here is an example- 975.9435 = 15*sqrt(5-(2*sqrt(5)))*((4*9)/sqrt(10+(2*sqrt(5))))^2.

How to calculate Total Surface Area of Great Dodecahedron given Circumsphere Radius?

With Circumsphere Radius of Great Dodecahedron (r_c) we can find Total Surface Area of Great Dodecahedron given Circumsphere Radius using the formula - Total Surface Area of Great Dodecahedron = 15*sqrt(5-(2*sqrt(5)))*((4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5))))^2. This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Great Dodecahedron?

Here are the different ways to Calculate Total Surface Area of Great Dodecahedron-

Total Surface Area of Great Dodecahedron=15*sqrt(5-(2*sqrt(5)))*Edge Length of Great Dodecahedron^2
Total Surface Area of Great Dodecahedron=15*sqrt(5-(2*sqrt(5)))*((2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1))^2
Total Surface Area of Great Dodecahedron=15*sqrt(5-(2*sqrt(5)))*((6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5))))^2

Can the Total Surface Area of Great Dodecahedron given Circumsphere Radius be negative?

No, the Total Surface Area of Great Dodecahedron given Circumsphere Radius, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Great Dodecahedron given Circumsphere Radius?

Total Surface Area of Great Dodecahedron given Circumsphere Radius is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Great Dodecahedron given Circumsphere Radius can be measured.

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