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Midsphere Radius of Icosahedron given Lateral Surface Area Formula

GoMidsphere Radius of Icosahedron Formula

GoMidsphere Radius of Icosahedron given Circumsphere Radius Formula

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The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere. Check FAQs

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot LSA}{9 \cdot \sqrt{3}}}

r_m - Midsphere Radius of Icosahedron?LSA - Lateral Surface Area of Icosahedron?

Midsphere Radius of Icosahedron given Lateral Surface Area Example

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

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

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

8.0932 = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

8.0932m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 780m²}{9 \cdot \sqrt{3}}}

8.0932 = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

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Midsphere Radius of Icosahedron given Lateral Surface Area Solution

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

FIRST Step Consider the formula

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot LSA}{9 \cdot \sqrt{3}}}

Next Step Substitute values of Variables

∴

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 780m²}{9 \cdot \sqrt{3}}}

Next Step Prepare to Evaluate

∴

r m = \frac{1 + \sqrt{5}}{4} \cdot \sqrt{\frac{2 \cdot 780}{9 \cdot \sqrt{3}}}

Next Step Evaluate

∴

r m = 8.093164639781m

LAST Step Rounding Answer

∴

r m = 8.0932m

Midsphere Radius of Icosahedron given Lateral Surface Area Formula Elements

Variables

Functions

Midsphere Radius of Icosahedron

The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron 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 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 Midsphere Radius of Icosahedron

Go Midsphere Radius of Icosahedron

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

Go Midsphere Radius of Icosahedron given Circumsphere Radius

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

Go Midsphere Radius of Icosahedron given Insphere Radius

r m = (1 + \sqrt{5}) \cdot \frac{3 \cdot r i}{\sqrt{3} \cdot (3 + \sqrt{5})}

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 Midsphere Radius of Icosahedron given Lateral Surface Area?

Midsphere Radius of Icosahedron given Lateral Surface Area evaluator uses Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))) to evaluate the Midsphere Radius of Icosahedron, The Midsphere Radius of Icosahedron given Lateral Surface Area formula is defined as the radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere and is calculated using the lateral surface area of the Icosahedron. Midsphere Radius of Icosahedron is denoted by r_m symbol.

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

FAQs on Midsphere Radius of Icosahedron given Lateral Surface Area

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

The formula of Midsphere Radius of Icosahedron given Lateral Surface Area is expressed as Midsphere Radius of Icosahedron = (1+sqrt(5))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))). Here is an example- 8.093165 = (1+sqrt(5))/4*sqrt((2*780)/(9*sqrt(3))).

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

With Lateral Surface Area of Icosahedron (LSA) we can find Midsphere Radius of Icosahedron given Lateral Surface Area using the formula - Midsphere Radius of Icosahedron = (1+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 Midsphere Radius of Icosahedron?

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

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

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

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

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

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

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