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Total Surface Area of Truncated Dodecahedron given Midsphere Radius Formula

GoTotal Surface Area of Truncated Dodecahedron Formula

GoTotal Surface Area of Truncated Dodecahedron given Dodecahedral Edge Length Formula

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

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot r m}{5 + (3 \cdot \sqrt{5})})}^{2}

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

Total Surface Area of Truncated Dodecahedron given Midsphere Radius Example

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

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

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

9913.2729 = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot 29}{5 + (3 \cdot \sqrt{5})})}^{2}

9913.2729m² = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot 29m}{5 + (3 \cdot \sqrt{5})})}^{2}

9913.2729 = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot 29}{5 + (3 \cdot \sqrt{5})})}^{2}

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Total Surface Area of Truncated Dodecahedron given Midsphere Radius Solution

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

FIRST Step Consider the formula

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot r m}{5 + (3 \cdot \sqrt{5})})}^{2}

Next Step Substitute values of Variables

∴

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot 29m}{5 + (3 \cdot \sqrt{5})})}^{2}

Next Step Prepare to Evaluate

∴

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot 29}{5 + (3 \cdot \sqrt{5})})}^{2}

Next Step Evaluate

∴

TSA = 9913.27292263569m²

LAST Step Rounding Answer

∴

TSA = 9913.2729m²

Total Surface Area of Truncated Dodecahedron given Midsphere Radius Formula Elements

Variables

Functions

Total Surface Area of Truncated Dodecahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Truncated Dodecahedron

Midsphere Radius of Truncated Dodecahedron

Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated Dodecahedron 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 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 Truncated Dodecahedron

Go Total Surface Area of Truncated Dodecahedron

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {l e}^{2}

Go Total Surface Area of Truncated Dodecahedron given Dodecahedral Edge Length

TSA = (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {l e(Dodecahedron)}^{2}

Go Total Surface Area of Truncated Dodecahedron given Volume

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{12 \cdot V}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{2}{3}}

Go Total Surface Area of Truncated Dodecahedron given Circumsphere Radius

TSA = 5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})})) \cdot {(\frac{4 \cdot r c}{\sqrt{74 + (30 \cdot \sqrt{5})}})}^{2}

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

Total Surface Area of Truncated Dodecahedron given Midsphere Radius evaluator uses Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^2 to evaluate the Total Surface Area of Truncated Dodecahedron, Total Surface Area of Truncated Dodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Dodecahedron, and calculated using the midsphere radius of the Truncated Dodecahedron. Total Surface Area of Truncated Dodecahedron is denoted by TSA symbol.

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

FAQs on Total Surface Area of Truncated Dodecahedron given Midsphere Radius

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

The formula of Total Surface Area of Truncated Dodecahedron given Midsphere Radius is expressed as Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^2. Here is an example- 9913.273 = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*29)/(5+(3*sqrt(5))))^2.

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

With Midsphere Radius of Truncated Dodecahedron (r_m) we can find Total Surface Area of Truncated Dodecahedron given Midsphere Radius using the formula - Total Surface Area of Truncated Dodecahedron = 5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((4*Midsphere Radius of Truncated Dodecahedron)/(5+(3*sqrt(5))))^2. This formula also uses Square Root (sqrt) function(s).

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

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

Total Surface Area of Truncated Dodecahedron=5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*Edge Length of Truncated Dodecahedron^2
Total Surface Area of Truncated Dodecahedron=(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*Dodecahedral Edge Length of Truncated Dodecahedron^2
Total Surface Area of Truncated Dodecahedron=5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(2/3)

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

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

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

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

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