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Total Surface Area of Icosahedron given Circumsphere Radius Formula

GoTotal Surface Area of Icosahedron Formula

GoTotal Surface Area of Icosahedron given Lateral Surface Area and Edge Length 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{4 \cdot r c}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

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

Total Surface Area of Icosahedron given Circumsphere Radius Example

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

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

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

775.5379 = 5 \cdot \sqrt{3} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

775.5379m² = 5 \cdot \sqrt{3} \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

775.5379 = 5 \cdot \sqrt{3} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

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Total Surface Area of Icosahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

TSA = 5 \cdot \sqrt{3} \cdot {(\frac{4 \cdot 9m}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 5 \cdot \sqrt{3} \cdot {(\frac{4 \cdot 9}{\sqrt{10 + (2 \cdot \sqrt{5})}})}^{2}

Next Step Evaluate

∴

TSA = 775.537852045189m²

LAST Step Rounding Answer

∴

TSA = 775.5379m²

Total Surface Area of Icosahedron given Circumsphere 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

Circumsphere Radius of Icosahedron

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

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

Go Total Surface Area of Icosahedron given Lateral Surface Area and Edge Length

TSA = LSA + \frac{\sqrt{3}}{2} \cdot {l e}^{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}}

Other formulas in Total Surface Area of Icosahedron category

Go Face Area of Icosahedron

A Face = \frac{\sqrt{3}}{4} \cdot {l e}^{2}

Go Face Area of Icosahedron given Circumsphere Radius

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

Go Face Area of Icosahedron given Total Surface Area

A Face = \frac{TSA}{20}

Go Lateral Surface Area of Icosahedron

LSA = 9 \cdot \frac{\sqrt{3}}{2} \cdot {l e}^{2}

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

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

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

FAQs on Total Surface Area of Icosahedron given Circumsphere Radius

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

The formula of Total Surface Area of Icosahedron given Circumsphere Radius is expressed as Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))^2. Here is an example- 775.5379 = 5*sqrt(3)*((4*9)/(sqrt(10+(2*sqrt(5)))))^2.

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

With Circumsphere Radius of Icosahedron (r_c) we can find Total Surface Area of Icosahedron given Circumsphere Radius using the formula - Total Surface Area of Icosahedron = 5*sqrt(3)*((4*Circumsphere Radius of Icosahedron)/(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 Icosahedron?

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

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

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

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

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

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

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