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Total Surface Area of Dodecahedron given Circumsphere Radius Formula

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GoTotal Surface Area of Dodecahedron given Volume Formula

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

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

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

Total Surface Area of Dodecahedron given Circumsphere Radius Example

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

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

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

2060.866 = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

2060.866m² = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

2060.866 = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

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Total Surface Area of Dodecahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot r c}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Substitute values of Variables

∴

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Evaluate

∴

TSA = 2060.865959507m²

LAST Step Rounding Answer

∴

TSA = 2060.866m²

Total Surface Area of Dodecahedron given Circumsphere Radius Formula Elements

Variables

Functions

Total Surface Area of Dodecahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Dodecahedron

Circumsphere Radius of Dodecahedron

Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the 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 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 Dodecahedron

Go Total Surface Area of Dodecahedron

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {l e}^{2}

Go Total Surface Area of Dodecahedron given Volume

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{2}{3}}

Go Total Surface Area of Dodecahedron given Face Diagonal

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot d Face}{1 + \sqrt{5}})}^{2}

Go Total Surface Area of Dodecahedron given Face Area

TSA = 12 \cdot A Face

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

Total Surface Area of Dodecahedron given Circumsphere Radius evaluator uses Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2 to evaluate the Total Surface Area of Dodecahedron, The Total Surface Area of Dodecahedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron, and calculated using circumsphere radius of Dodecahedron. Total Surface Area of Dodecahedron is denoted by TSA symbol.

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

FAQs on Total Surface Area of Dodecahedron given Circumsphere Radius

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

The formula of Total Surface Area of Dodecahedron given Circumsphere Radius is expressed as Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2. Here is an example- 2060.866 = 3*sqrt(25+(10*sqrt(5)))*((4*14)/(sqrt(3)*(1+sqrt(5))))^2.

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

With Circumsphere Radius of Dodecahedron (r_c) we can find Total Surface Area of Dodecahedron given Circumsphere Radius using the formula - Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2. This formula also uses Square Root (sqrt) function(s).

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

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

Total Surface Area of Dodecahedron=3*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Total Surface Area of Dodecahedron=3*sqrt(25+(10*sqrt(5)))*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(2/3)
Total Surface Area of Dodecahedron=3*sqrt(25+(10*sqrt(5)))*((2*Face Diagonal of Dodecahedron)/(1+sqrt(5)))^2

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

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

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

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

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