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Total Surface Area of Truncated Icosahedron given Midsphere Radius Formula

GoTotal Surface Area of Truncated Icosahedron Formula

GoTotal Surface Area of Truncated Icosahedron given Icosahedral Edge Length Formula

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

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

TSA - Total Surface Area of Truncated Icosahedron?r_m - Midsphere Radius of Truncated Icosahedron?

Total Surface Area of Truncated Icosahedron given Midsphere Radius Example

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

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

7099.7767 = 3 \cdot {(\frac{4 \cdot 24}{3 \cdot (1 + \sqrt{5})})}^{2} \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})

7099.7767m² = 3 \cdot {(\frac{4 \cdot 24m}{3 \cdot (1 + \sqrt{5})})}^{2} \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})

7099.7767 = 3 \cdot {(\frac{4 \cdot 24}{3 \cdot (1 + \sqrt{5})})}^{2} \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})

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Total Surface Area of Truncated Icosahedron given Midsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

TSA = 3 \cdot {(\frac{4 \cdot 24m}{3 \cdot (1 + \sqrt{5})})}^{2} \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})

Next Step Prepare to Evaluate

∴

TSA = 3 \cdot {(\frac{4 \cdot 24}{3 \cdot (1 + \sqrt{5})})}^{2} \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})

Next Step Evaluate

∴

TSA = 7099.77672429446m²

LAST Step Rounding Answer

∴

TSA = 7099.7767m²

Total Surface Area of Truncated Icosahedron given Midsphere Radius Formula Elements

Variables

Functions

Total Surface Area of Truncated Icosahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Truncated Icosahedron

Midsphere Radius of Truncated Icosahedron

Midsphere Radius of Truncated Icosahedron is the radius of the sphere for which all the edges of the Truncated Icosahedron become a tangent line on that sphere.

Symbol: r_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Midsphere Radius of Truncated 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 Truncated Icosahedron

Go Total Surface Area of Truncated Icosahedron

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

Go Total Surface Area of Truncated Icosahedron given Icosahedral Edge Length

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

Go Total Surface Area of Truncated Icosahedron given Volume

TSA = 3 \cdot {(\frac{4 \cdot V}{125 + (43 \cdot \sqrt{5})})}^{\frac{2}{3}} \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})

Go Total Surface Area of Truncated Icosahedron given Circumsphere Radius

TSA = 3 \cdot {(\frac{4 \cdot r c}{\sqrt{58 + (18 \cdot \sqrt{5})}})}^{2} \cdot ((10 \cdot \sqrt{3}) + \sqrt{25 + (10 \cdot \sqrt{5})})

How to Evaluate Total Surface Area of Truncated Icosahedron given Midsphere Radius?

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

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

FAQs on Total Surface Area of Truncated Icosahedron given Midsphere Radius

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

The formula of Total Surface Area of Truncated Icosahedron given Midsphere Radius is expressed as Total Surface Area of Truncated Icosahedron = 3*((4*Midsphere Radius of Truncated Icosahedron)/(3*(1+sqrt(5))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))). Here is an example- 7099.777 = 3*((4*24)/(3*(1+sqrt(5))))^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5)))).

How to calculate Total Surface Area of Truncated Icosahedron given Midsphere Radius?

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

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

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

Total Surface Area of Truncated Icosahedron=3*Edge Length of Truncated Icosahedron^2*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Total Surface Area of Truncated Icosahedron=(Icosahedral Edge Length of Truncated Icosahedron^2)/3*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))
Total Surface Area of Truncated Icosahedron=3*((4*Volume of Truncated Icosahedron)/(125+(43*sqrt(5))))^(2/3)*((10*sqrt(3))+sqrt(25+(10*sqrt(5))))

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

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

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

Total Surface Area of Truncated Icosahedron given Midsphere 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 Icosahedron given Midsphere Radius can be measured.

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