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Total Surface Area of Pentakis Dodecahedron given Insphere Radius Formula

GoTotal Surface Area of Pentakis Dodecahedron Formula

GoTotal Surface Area of Pentakis Dodecahedron given Leg Length Formula

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Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron. Check FAQs

TSA = (\frac{15}{19}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})}) \cdot ({(\frac{2 \cdot r i}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{2})

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

Total Surface Area of Pentakis Dodecahedron given Insphere Radius Example

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

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

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

1925.6611 = (\frac{15}{19}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})}) \cdot ({(\frac{2 \cdot 12}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{2})

1925.6611m² = (\frac{15}{19}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})}) \cdot ({(\frac{2 \cdot 12m}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{2})

1925.6611 = (\frac{15}{19}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})}) \cdot ({(\frac{2 \cdot 12}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{2})

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Total Surface Area of Pentakis Dodecahedron given Insphere Radius Solution

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

FIRST Step Consider the formula

TSA = (\frac{15}{19}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})}) \cdot ({(\frac{2 \cdot r i}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{2})

Next Step Substitute values of Variables

∴

TSA = (\frac{15}{19}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})}) \cdot ({(\frac{2 \cdot 12m}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{2})

Next Step Prepare to Evaluate

∴

TSA = (\frac{15}{19}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})}) \cdot ({(\frac{2 \cdot 12}{3 \cdot (\sqrt{\frac{81 + (35 \cdot \sqrt{5})}{218}})})}^{2})

Next Step Evaluate

∴

TSA = 1925.66109639037m²

LAST Step Rounding Answer

∴

TSA = 1925.6611m²

Total Surface Area of Pentakis Dodecahedron given Insphere Radius Formula Elements

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Total Surface Area of Pentakis Dodecahedron

Total Surface Area of Pentakis Dodecahedron is the amount or quantity of two dimensional space covered on the surface of Pentakis Dodecahedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Pentakis Dodecahedron

Insphere Radius of Pentakis Dodecahedron

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

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere Radius of Pentakis 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 Pentakis Dodecahedron

Go Total Surface Area of Pentakis Dodecahedron

TSA = (\frac{15}{19}) \cdot ({l Base}^{2}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})})

Go Total Surface Area of Pentakis Dodecahedron given Leg Length

TSA = (\frac{15}{19}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})}) \cdot ({(\frac{38 \cdot l Leg}{3 \cdot (9 + \sqrt{5})})}^{2})

Go Total Surface Area of Pentakis Dodecahedron given Volume

TSA = (\frac{15}{19}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})}) \cdot ({(\frac{76 \cdot V}{15 \cdot (23 + (11 \cdot \sqrt{5}))})}^{\frac{2}{3}})

Go Total Surface Area of Pentakis Dodecahedron given Midsphere Radius

TSA = (\frac{15}{19}) \cdot (\sqrt{413 + (162 \cdot \sqrt{5})}) \cdot ({(\frac{4 \cdot r m}{3 + \sqrt{5}})}^{2})

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

Total Surface Area of Pentakis Dodecahedron given Insphere Radius evaluator uses Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2) to evaluate the Total Surface Area of Pentakis Dodecahedron, Total Surface Area of Pentakis Dodecahedron given Insphere Radius formula is defined as the amount or quantity of two-dimensional space covered on the surface of the Pentakis Dodecahedron, calculated using insphere radius of Pentakis Dodecahedron. Total Surface Area of Pentakis Dodecahedron is denoted by TSA symbol.

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

FAQs on Total Surface Area of Pentakis Dodecahedron given Insphere Radius

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

The formula of Total Surface Area of Pentakis Dodecahedron given Insphere Radius is expressed as Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2). Here is an example- 1925.661 = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*12)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2).

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

With Insphere Radius of Pentakis Dodecahedron (r_i) we can find Total Surface Area of Pentakis Dodecahedron given Insphere Radius using the formula - Total Surface Area of Pentakis Dodecahedron = (15/19)*(sqrt(413+(162*sqrt(5))))*(((2*Insphere Radius of Pentakis Dodecahedron)/(3*(sqrt((81+(35*sqrt(5)))/218))))^2). This formula also uses Square Root (sqrt) function(s).

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

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

Total Surface Area of Pentakis Dodecahedron=(15/19)*(Base Length of Pentakis Dodecahedron^2)*(sqrt(413+(162*sqrt(5))))
Total Surface Area of Pentakis Dodecahedron=(15/19)*(sqrt(413+(162*sqrt(5))))*(((38*Leg Length of Pentakis Dodecahedron)/(3*(9+sqrt(5))))^2)
Total Surface Area of Pentakis Dodecahedron=(15/19)*(sqrt(413+(162*sqrt(5))))*(((76*Volume of Pentakis Dodecahedron)/(15*(23+(11*sqrt(5)))))^(2/3))

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

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

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

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

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