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Insphere Radius of Icosahedron given Lateral Surface Area Formula

GoInsphere Radius of Icosahedron Formula

GoInsphere Radius of Icosahedron given Total Surface Area Formula

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Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere. Check FAQs

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{2 \cdot LSA}{9 \cdot \sqrt{3}}}

r_i - Insphere Radius of Icosahedron?LSA - Lateral Surface Area of Icosahedron?

Insphere Radius of Icosahedron given Lateral Surface Area Example

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

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

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

7.5604 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

7.5604m = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{2 \cdot 780m²}{9 \cdot \sqrt{3}}}

7.5604 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

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Insphere Radius of Icosahedron given Lateral Surface Area Solution

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

FIRST Step Consider the formula

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{2 \cdot LSA}{9 \cdot \sqrt{3}}}

Next Step Substitute values of Variables

∴

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{2 \cdot 780m²}{9 \cdot \sqrt{3}}}

Next Step Prepare to Evaluate

∴

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

Next Step Evaluate

∴

r i = 7.56041070301785m

LAST Step Rounding Answer

∴

r i = 7.5604m

Insphere Radius of Icosahedron given Lateral Surface Area Formula Elements

Variables

Functions

Insphere Radius of Icosahedron

Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Insphere 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 Insphere Radius of Icosahedron

Go Insphere Radius of Icosahedron

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot l e

Go Insphere Radius of Icosahedron given Total Surface Area

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{TSA}{5 \cdot \sqrt{3}}}

Go Insphere Radius of Icosahedron given Surface to Volume Ratio

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \frac{12 \cdot \sqrt{3}}{(3 + \sqrt{5}) \cdot R A/V}

Go Insphere Radius of Icosahedron given Circumsphere Radius

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

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

Insphere Radius of Icosahedron given Lateral Surface Area evaluator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))) to evaluate the Insphere Radius of Icosahedron, The Insphere Radius of Icosahedron given Lateral Surface Area formula is defined as the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere, and calculated using the lateral surface area of the Icosahedron. Insphere Radius of Icosahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Icosahedron given Lateral Surface Area

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

The formula of Insphere Radius of Icosahedron given Lateral Surface Area is expressed as Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))). Here is an example- 7.560411 = (sqrt(3)*(3+sqrt(5)))/12*sqrt((2*780)/(9*sqrt(3))).

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

With Lateral Surface Area of Icosahedron (LSA) we can find Insphere Radius of Icosahedron given Lateral Surface Area using the formula - Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*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 Insphere Radius of Icosahedron?

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

Insphere Radius of Icosahedron=(sqrt(3)*(3+sqrt(5)))/12*Edge Length of Icosahedron
Insphere Radius of Icosahedron=(sqrt(3)*(3+sqrt(5)))/12*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Insphere Radius of Icosahedron=(sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)

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

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

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

Insphere 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 Insphere Radius of Icosahedron given Lateral Surface Area can be measured.

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