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Lateral Surface Area of Dodecahedron given Circumsphere Radius Formula

GoLateral Surface Area of Dodecahedron Formula

GoLateral Surface Area of Dodecahedron given Total Surface Area Formula

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Lateral Surface Area of Dodecahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron. Check FAQs

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

LSA - Lateral Surface Area of Dodecahedron?r_c - Circumsphere Radius of Dodecahedron?

Lateral Surface Area of Dodecahedron given Circumsphere Radius Example

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

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

Here is how the Lateral Surface Area of Dodecahedron given Circumsphere Radius equation looks like.

1717.3883 = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

1717.3883m² = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

1717.3883 = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

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Lateral Surface Area of Dodecahedron given Circumsphere Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14m}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Prepare to Evaluate

∴

LSA = \frac{5}{2} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot 14}{\sqrt{3} \cdot (1 + \sqrt{5})})}^{2}

Next Step Evaluate

∴

LSA = 1717.38829958917m²

LAST Step Rounding Answer

∴

LSA = 1717.3883m²

Lateral Surface Area of Dodecahedron given Circumsphere Radius Formula Elements

Variables

Functions

Lateral Surface Area of Dodecahedron

Lateral Surface Area of Dodecahedron is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron.

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral Surface Area of Dodecahedron

Circumsphere Radius of Dodecahedron

Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron 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 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 Lateral Surface Area of Dodecahedron

Go Lateral Surface Area of Dodecahedron

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

Go Lateral Surface Area of Dodecahedron given Total Surface Area

LSA = \frac{5}{6} \cdot TSA

Other formulas in Lateral Surface Area of Dodecahedron category

Go Face Area of Dodecahedron

A Face = \frac{1}{4} \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {l e}^{2}

Go Face Area of Dodecahedron given Midsphere Radius

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

Go Total Surface Area of Dodecahedron

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

Go Total Surface Area of Dodecahedron given Volume

TSA = 3 \cdot \sqrt{25 + (10 \cdot \sqrt{5})} \cdot {(\frac{4 \cdot V}{15 + (7 \cdot \sqrt{5})})}^{\frac{2}{3}}

How to Evaluate Lateral Surface Area of Dodecahedron given Circumsphere Radius?

Lateral Surface Area of Dodecahedron given Circumsphere Radius evaluator uses Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2 to evaluate the Lateral Surface Area of Dodecahedron, The Lateral Surface Area of Dodecahedron given Circumsphere Radius formula is defined as the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Dodecahedron, and calculated using circumsphere radius of Dodecahedron. Lateral Surface Area of Dodecahedron is denoted by LSA symbol.

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

FAQs on Lateral Surface Area of Dodecahedron given Circumsphere Radius

What is the formula to find Lateral Surface Area of Dodecahedron given Circumsphere Radius?

The formula of Lateral Surface Area of Dodecahedron given Circumsphere Radius is expressed as Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2. Here is an example- 1717.388 = 5/2*sqrt(25+(10*sqrt(5)))*((4*14)/(sqrt(3)*(1+sqrt(5))))^2.

How to calculate Lateral Surface Area of Dodecahedron given Circumsphere Radius?

With Circumsphere Radius of Dodecahedron (r_c) we can find Lateral Surface Area of Dodecahedron given Circumsphere Radius using the formula - Lateral Surface Area of Dodecahedron = 5/2*sqrt(25+(10*sqrt(5)))*((4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))))^2. This formula also uses Square Root (sqrt) function(s).

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

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

Lateral Surface Area of Dodecahedron=5/2*sqrt(25+(10*sqrt(5)))*Edge Length of Dodecahedron^2
Lateral Surface Area of Dodecahedron=5/6*Total Surface Area of Dodecahedron

Can the Lateral Surface Area of Dodecahedron given Circumsphere Radius be negative?

No, the Lateral Surface Area of Dodecahedron given Circumsphere Radius, measured in Area cannot be negative.

Which unit is used to measure Lateral Surface Area of Dodecahedron given Circumsphere Radius?

Lateral Surface Area of Dodecahedron 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 Lateral Surface Area of Dodecahedron given Circumsphere Radius can be measured.

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