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Total Surface Area of Truncated Dodecahedron given Circumsphere Radius Formula

GoTotal Surface Area of Truncated Dodecahedron Formula

GoTotal Surface Area of Truncated Dodecahedron given Dodecahedral Edge Length Formula

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

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot r c}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{2}

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

Total Surface Area of Truncated Dodecahedron given Circumsphere Radius Example

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

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

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

10307.9524 = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot 30}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{2}

10307.9524m² = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot 30m}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{2}

10307.9524 = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot 30}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{2}

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Total Surface Area of Truncated Dodecahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot r c}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{2}

Next Step Substitute values of Variables

∴

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot 30m}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot 30}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{2}

Next Step Evaluate

∴

TSA = 10307.9524024646m²

LAST Step Rounding Answer

∴

TSA = 10307.9524m²

Total Surface Area of Truncated Dodecahedron given Circumsphere Radius Formula Elements

Variables

Functions

Total Surface Area of Truncated Dodecahedron

Total Surface Area of Truncated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Truncated Dodecahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Truncated Dodecahedron

Circumsphere Radius of Truncated Dodecahedron

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

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of Truncated 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 Truncated Dodecahedron

Go Total Surface Area of Truncated Dodecahedron

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {l e}^{2}

Go Total Surface Area of Truncated Dodecahedron given Dodecahedral Edge Length

TSA = (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {l e(Dodecahedron)}^{2}

Go Total Surface Area of Truncated Dodecahedron given Volume

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{12 \cdot V}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{2}{3}}

Go Total Surface Area of Truncated Dodecahedron given Midsphere Radius

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot r m}{5 + (3 \cdot \sqrt{5})})}^{2}

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

Total Surface Area of Truncated Dodecahedron given Circumsphere Radius evaluator uses Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^2 to evaluate the Total Surface Area of Truncated Dodecahedron, Total Surface Area of Truncated Dodecahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Dodecahedron, and calculated using the circumsphere radius of the Truncated Dodecahedron. Total Surface Area of Truncated Dodecahedron is denoted by TSA symbol.

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

FAQs on Total Surface Area of Truncated Dodecahedron given Circumsphere Radius

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

The formula of Total Surface Area of Truncated Dodecahedron given Circumsphere Radius is expressed as Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^2. Here is an example- 10307.95 = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*30)/(sqrt(74+(30*sqrt(5)))))^2.

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

With Circumsphere Radius of Truncated Dodecahedron (r_c) we can find Total Surface Area of Truncated Dodecahedron given Circumsphere Radius using the formula - Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Circumsphere Radius of Truncated Dodecahedron)/(sqrt(74+(30*sqrt(5)))))^2. This formula also uses Square Root (sqrt) function(s).

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

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

Total Surface Area of Truncated Dodecahedron=5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*Edge Length of Truncated Dodecahedron^2
Total Surface Area of Truncated Dodecahedron=(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*Dodecahedral Edge Length of Truncated Dodecahedron^2
Total Surface Area of Truncated Dodecahedron=5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(2/3)

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

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

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

Total Surface Area of Truncated 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 Truncated Dodecahedron given Circumsphere Radius can be measured.

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