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Total Surface Area of Icosahedron given Insphere Radius Formula

GoTotal Surface Area of Icosahedron given Circumsphere Radius Formula

GoTotal Surface Area of Icosahedron given Volume Formula

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

TSA = 5 \cdot \sqrt{3} \cdot {(\frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

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

Total Surface Area of Icosahedron given Insphere Radius Example

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

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

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

742.9463 = 5 \cdot \sqrt{3} \cdot {(\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

742.9463m² = 5 \cdot \sqrt{3} \cdot {(\frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

742.9463 = 5 \cdot \sqrt{3} \cdot {(\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

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Total Surface Area of Icosahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

TSA = 5 \cdot \sqrt{3} \cdot {(\frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

Next Step Substitute values of Variables

∴

TSA = 5 \cdot \sqrt{3} \cdot {(\frac{12 \cdot 7m}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 5 \cdot \sqrt{3} \cdot {(\frac{12 \cdot 7}{\sqrt{3} \cdot (3 + \sqrt{5})})}^{2}

Next Step Evaluate

∴

TSA = 742.946253109039m²

LAST Step Rounding Answer

∴

TSA = 742.9463m²

Total Surface Area of Icosahedron given Insphere Radius Formula Elements

Variables

Functions

Total Surface Area of Icosahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Icosahedron

Insphere Radius of Icosahedron

Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron 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 Icosahedron

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 Icosahedron

Go Total Surface Area of Icosahedron given Circumsphere Radius

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

Go Total Surface Area of Icosahedron given Volume

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

Go Total Surface Area of Icosahedron

TSA = 5 \cdot \sqrt{3} \cdot {l e}^{2}

Go Total Surface Area of Icosahedron given Midsphere Radius

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

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

Total Surface Area of Icosahedron given Insphere Radius evaluator uses Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2 to evaluate the Total Surface Area of Icosahedron, The Total Surface Area of Icosahedron given Insphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Icosahedron and calculated using the insphere radius of the Icosahedron. Total Surface Area of Icosahedron is denoted by TSA symbol.

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

FAQs on Total Surface Area of Icosahedron given Insphere Radius

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

The formula of Total Surface Area of Icosahedron given Insphere Radius is expressed as Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2. Here is an example- 742.9463 = 5*sqrt(3)*((12*7)/(sqrt(3)*(3+sqrt(5))))^2.

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

With Insphere Radius of Icosahedron (r_i) we can find Total Surface Area of Icosahedron given Insphere Radius using the formula - Total Surface Area of Icosahedron = 5*sqrt(3)*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5))))^2. This formula also uses Square Root (sqrt) function(s).

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

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

Total Surface Area of Icosahedron=5*sqrt(3)*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2
Total Surface Area of Icosahedron=5*sqrt(3)*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(2/3)
Total Surface Area of Icosahedron=5*sqrt(3)*Edge Length of Icosahedron^2

Can the Total Surface Area of Icosahedron given Insphere Radius be negative?

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

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

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

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