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Total Surface Area of Snub Dodecahedron given Midsphere Radius Formula

GoTotal Surface Area of Snub Dodecahedron Formula

GoTotal Surface Area of Snub Dodecahedron given Volume Formula

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

TSA = ((20 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})) \cdot {(\frac{2 \cdot r m}{\sqrt{\frac{1}{1 - 0.94315125924}}})}^{2}

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

Total Surface Area of Snub Dodecahedron given Midsphere Radius Example

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

5544.22 = ((20 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})) \cdot {(\frac{2 \cdot 21}{\sqrt{\frac{1}{1 - 0.94315125924}}})}^{2}

5544.22m² = ((20 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})) \cdot {(\frac{2 \cdot 21m}{\sqrt{\frac{1}{1 - 0.94315125924}}})}^{2}

5544.22 = ((20 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})) \cdot {(\frac{2 \cdot 21}{\sqrt{\frac{1}{1 - 0.94315125924}}})}^{2}

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Total Surface Area of Snub Dodecahedron given Midsphere Radius Solution

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

FIRST Step Consider the formula

TSA = ((20 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})) \cdot {(\frac{2 \cdot r m}{\sqrt{\frac{1}{1 - 0.94315125924}}})}^{2}

Next Step Substitute values of Variables

∴

TSA = ((20 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})) \cdot {(\frac{2 \cdot 21m}{\sqrt{\frac{1}{1 - 0.94315125924}}})}^{2}

Next Step Prepare to Evaluate

∴

TSA = ((20 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})) \cdot {(\frac{2 \cdot 21}{\sqrt{\frac{1}{1 - 0.94315125924}}})}^{2}

Next Step Evaluate

∴

TSA = 5544.21995095455m²

LAST Step Rounding Answer

∴

TSA = 5544.22m²

Total Surface Area of Snub Dodecahedron given Midsphere Radius Formula Elements

Variables

Functions

Total Surface Area of Snub Dodecahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Snub Dodecahedron

Midsphere Radius of Snub Dodecahedron

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

Go Total Surface Area of Snub Dodecahedron

TSA = ((20 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})) \cdot {l e}^{2}

Go Total Surface Area of Snub Dodecahedron given Volume

TSA = ((20 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})) \cdot {(\frac{V \cdot 6 \cdot {(3 - {({(\frac{[phi]}{2} + \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}} + {(\frac{[phi]}{2} - \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}})}^{2})}^{\frac{3}{2}}}{((12 \cdot ((3 \cdot [phi]) + 1)) \cdot ({({(\frac{[phi]}{2} + \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}} + {(\frac{[phi]}{2} - \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}})}^{2}) - (((36 \cdot [phi]) + 7) \cdot ({(\frac{[phi]}{2} + \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}} + {(\frac{[phi]}{2} - \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}}))) - ((53 \cdot [phi]) + 6)})}^{\frac{2}{3}}

Other formulas in Total Surface Area of Snub Dodecahedron category

Go Circumsphere Radius of Snub Dodecahedron

r c = \frac{\sqrt{\frac{2 - 0.94315125924}{1 - 0.94315125924}}}{2} \cdot l e

Go Midsphere Radius of Snub Dodecahedron

r m = \frac{\sqrt{\frac{1}{1 - 0.94315125924}}}{2} \cdot l e

Go Surface to Volume Ratio of Snub Dodecahedron

R A/V = \frac{((20 \cdot \sqrt{3}) + (3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})})) \cdot 6 \cdot {(3 - {({(\frac{[phi]}{2} + \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}} + {(\frac{[phi]}{2} - \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}})}^{2})}^{\frac{3}{2}}}{l e \cdot (((12 \cdot ((3 \cdot [phi]) + 1)) \cdot ({({(\frac{[phi]}{2} + \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}} + {(\frac{[phi]}{2} - \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}})}^{2}) - (((36 \cdot [phi]) + 7) \cdot ({(\frac{[phi]}{2} + \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}} + {(\frac{[phi]}{2} - \frac{\sqrt{[phi] - \frac{5}{27}}}{2})}^{\frac{1}{3}}))) - ((53 \cdot [phi]) + 6))}

Go Edge Length of Snub Dodecahedron given Circumsphere Radius

l e = \frac{2 \cdot r c}{\sqrt{\frac{2 - 0.94315125924}{1 - 0.94315125924}}}

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

Total Surface Area of Snub Dodecahedron given Midsphere Radius evaluator uses Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924)))^2 to evaluate the Total Surface Area of Snub Dodecahedron, Total Surface Area of Snub Dodecahedron given Midsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Snub Dodecahedron, and calculated using the midsphere radius of the Snub Dodecahedron. Total Surface Area of Snub Dodecahedron is denoted by TSA symbol.

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

FAQs on Total Surface Area of Snub Dodecahedron given Midsphere Radius

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

The formula of Total Surface Area of Snub Dodecahedron given Midsphere Radius is expressed as Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924)))^2. Here is an example- 5544.22 = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*21)/sqrt(1/(1-0.94315125924)))^2.

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

With Midsphere Radius of Snub Dodecahedron (r_m) we can find Total Surface Area of Snub Dodecahedron given Midsphere Radius using the formula - Total Surface Area of Snub Dodecahedron = ((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((2*Midsphere Radius of Snub Dodecahedron)/sqrt(1/(1-0.94315125924)))^2. This formula also uses Square Root (sqrt) function(s).

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

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

Total Surface Area of Snub Dodecahedron=((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*Edge Length of Snub Dodecahedron^2
Total Surface Area of Snub Dodecahedron=((20*sqrt(3))+(3*sqrt(25+(10*sqrt(5)))))*((Volume of Snub Dodecahedron*6*(3-(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)^(3/2))/(((12*((3*[phi])+1))*((([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))^2)-(((36*[phi])+7)*(([phi]/2+sqrt([phi]-5/27)/2)^(1/3)+([phi]/2-sqrt([phi]-5/27)/2)^(1/3))))-((53*[phi])+6)))^(2/3)

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

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

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

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

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