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Total Surface Area of Dodecahedron given Insphere Radius Formula

GoTotal Surface Area of Dodecahedron Formula

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{2 \cdot r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

TSA - Total Surface Area of Dodecahedron?r_i - Insphere Radius of Dodecahedron?

Total Surface Area of Dodecahedron given Insphere Radius Example

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

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

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

2014.7556 = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

2014.7556m² = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

2014.7556 = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

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Total Surface Area of Dodecahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot r i}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

Next Step Substitute values of Variables

∴

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11m}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{2 \cdot 11}{\sqrt{\frac{25 + (11 \cdot \sqrt{5})}{10}}})}^{2}

Next Step Evaluate

∴

TSA = 2014.75564335113m²

LAST Step Rounding Answer

∴

TSA = 2014.7556m²

Total Surface Area of Dodecahedron given Insphere 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

Insphere Radius of Dodecahedron

Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere 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 Circumsphere Radius

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

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

Total Surface Area of Dodecahedron given Insphere Radius evaluator uses Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2 to evaluate the Total Surface Area of Dodecahedron, The Total Surface Area of Dodecahedron given Insphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Dodecahedron, and calculated using insphere radius of Dodecahedron. Total Surface Area of Dodecahedron is denoted by TSA symbol.

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

FAQs on Total Surface Area of Dodecahedron given Insphere Radius

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

The formula of Total Surface Area of Dodecahedron given Insphere Radius is expressed as Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^2. Here is an example- 2014.756 = 3*sqrt(25+(10*sqrt(5)))*((2*11)/(sqrt((25+(11*sqrt(5)))/10)))^2.

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

With Insphere Radius of Dodecahedron (r_i) we can find Total Surface Area of Dodecahedron given Insphere Radius using the formula - Total Surface Area of Dodecahedron = 3*sqrt(25+(10*sqrt(5)))*((2*Insphere Radius of Dodecahedron)/(sqrt((25+(11*sqrt(5)))/10)))^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 Insphere Radius be negative?

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

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

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

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