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Circumsphere Radius of Icosahedron given Lateral Surface Area Formula

GoCircumsphere Radius of Icosahedron Formula

GoCircumsphere Radius of Icosahedron given Insphere Radius Formula

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Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere. Check FAQs

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{2 \cdot LSA}{9 \cdot \sqrt{3}}}

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

Circumsphere Radius of Icosahedron given Lateral Surface Area Example

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

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

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

9.5141 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

9.5141m = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{2 \cdot 780m²}{9 \cdot \sqrt{3}}}

9.5141 = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

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Circumsphere Radius of Icosahedron given Lateral Surface Area Solution

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

FIRST Step Consider the formula

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{2 \cdot LSA}{9 \cdot \sqrt{3}}}

Next Step Substitute values of Variables

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{2 \cdot 780m²}{9 \cdot \sqrt{3}}}

Next Step Prepare to Evaluate

∴

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

Next Step Evaluate

∴

r c = 9.51408563927639m

LAST Step Rounding Answer

∴

r c = 9.5141m

Circumsphere Radius of Icosahedron given Lateral Surface Area Formula Elements

Variables

Functions

Circumsphere Radius of Icosahedron

Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron 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 Icosahedron

Lateral Surface Area of Icosahedron

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

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral Surface Area of 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 Circumsphere Radius of Icosahedron

Go Circumsphere Radius of Icosahedron

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot l e

Go Circumsphere Radius of Icosahedron given Insphere Radius

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})}

Go Circumsphere Radius of Icosahedron given Midsphere Radius

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{4 \cdot r m}{1 + \sqrt{5}}

Go Circumsphere Radius of Icosahedron given Surface to Volume Ratio

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot R A/V}

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

Circumsphere Radius of Icosahedron given Lateral Surface Area evaluator uses Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))) to evaluate the Circumsphere Radius of Icosahedron, The Circumsphere Radius of Icosahedron given Lateral Surface Area formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the lateral surface area of the Icosahedron. Circumsphere Radius of Icosahedron is denoted by r_c symbol.

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

FAQs on Circumsphere Radius of Icosahedron given Lateral Surface Area

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

The formula of Circumsphere Radius of Icosahedron given Lateral Surface Area is expressed as Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))). Here is an example- 9.514086 = sqrt(10+(2*sqrt(5)))/4*sqrt((2*780)/(9*sqrt(3))).

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

With Lateral Surface Area of Icosahedron (LSA) we can find Circumsphere Radius of Icosahedron given Lateral Surface Area using the formula - Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Circumsphere Radius of Icosahedron?

Here are the different ways to Calculate Circumsphere Radius of Icosahedron-

Circumsphere Radius of Icosahedron=sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron
Circumsphere Radius of Icosahedron=sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Circumsphere Radius of Icosahedron=sqrt(10+(2*sqrt(5)))/4*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))

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

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

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

Circumsphere Radius of Icosahedron given Lateral Surface Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Circumsphere Radius of Icosahedron given Lateral Surface Area can be measured.

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