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Insphere Radius of Icosahedron given Total Surface Area Formula

GoInsphere Radius of Icosahedron 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{TSA}{5 \cdot \sqrt{3}}}

r_i - Insphere Radius of Icosahedron?TSA - Total Surface Area of Icosahedron?

Insphere Radius of Icosahedron given Total Surface Area Example

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

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

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

7.5749 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{870}{5 \cdot \sqrt{3}}}

7.5749m = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{870m²}{5 \cdot \sqrt{3}}}

7.5749 = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{870}{5 \cdot \sqrt{3}}}

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Insphere Radius of Icosahedron given Total Surface Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{870m²}{5 \cdot \sqrt{3}}}

Next Step Prepare to Evaluate

∴

r i = \frac{\sqrt{3} \cdot (3 + \sqrt{5})}{12} \cdot \sqrt{\frac{870}{5 \cdot \sqrt{3}}}

Next Step Evaluate

∴

r i = 7.57493600114069m

LAST Step Rounding Answer

∴

r i = 7.5749m

Insphere Radius of Icosahedron given Total 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

Total Surface Area of Icosahedron

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total 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

Other formulas in Insphere Radius of Icosahedron category

Go Circumsphere Radius of Icosahedron

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

Go Circumsphere Radius of Icosahedron given Volume

r c = \frac{\sqrt{10 + (2 \cdot \sqrt{5})}}{4} \cdot {(\frac{12 \cdot V}{5 \cdot (3 + \sqrt{5})})}^{\frac{1}{3}}

Go Midsphere Radius of Icosahedron

r m = \frac{1 + \sqrt{5}}{4} \cdot l e

Go Midsphere Radius of Icosahedron given Space Diagonal

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

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

Insphere Radius of Icosahedron given Total Surface Area evaluator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3))) to evaluate the Insphere Radius of Icosahedron, Insphere Radius of Icosahedron given Total 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 total surface area of the Icosahedron. Insphere Radius of Icosahedron is denoted by r_i symbol.

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

FAQs on Insphere Radius of Icosahedron given Total Surface Area

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

The formula of Insphere Radius of Icosahedron given Total Surface Area is expressed as Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3))). Here is an example- 7.574936 = (sqrt(3)*(3+sqrt(5)))/12*sqrt(870/(5*sqrt(3))).

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

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

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

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

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

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

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