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Midsphere Radius of Truncated Dodecahedron given Volume Formula

GoMidsphere Radius of Truncated Dodecahedron Formula

GoMidsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length Formula

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Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere. Check FAQs

r m = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot {(\frac{12 \cdot V}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

r_m - Midsphere Radius of Truncated Dodecahedron?V - Volume of Truncated Dodecahedron?

Midsphere Radius of Truncated Dodecahedron given Volume Example

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Here is how the Midsphere Radius of Truncated Dodecahedron given Volume equation looks like with Values.

Here is how the Midsphere Radius of Truncated Dodecahedron given Volume equation looks like with Units.

Here is how the Midsphere Radius of Truncated Dodecahedron given Volume equation looks like.

29.266 = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot {(\frac{12 \cdot 85000}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

29.266m = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot {(\frac{12 \cdot 85000m³}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

29.266 = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot {(\frac{12 \cdot 85000}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

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Midsphere Radius of Truncated Dodecahedron given Volume Solution

Follow our step by step solution on how to calculate Midsphere Radius of Truncated Dodecahedron given Volume?

FIRST Step Consider the formula

r m = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot {(\frac{12 \cdot V}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

r m = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot {(\frac{12 \cdot 85000m³}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

r m = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot {(\frac{12 \cdot 85000}{5 \cdot (99 + (47 \cdot \sqrt{5}))})}^{\frac{1}{3}}

Next Step Evaluate

∴

r m = 29.2659582986027m

LAST Step Rounding Answer

∴

r m = 29.266m

Midsphere Radius of Truncated Dodecahedron given Volume Formula Elements

Variables

Functions

Midsphere Radius of Truncated Dodecahedron

Midsphere Radius of Truncated Dodecahedron is the radius of the sphere for which all the edges of the Truncated Dodecahedron 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 Truncated Dodecahedron

Volume of Truncated Dodecahedron

Volume of Truncated Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Truncated Dodecahedron.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Truncated 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 Midsphere Radius of Truncated Dodecahedron

Go Midsphere Radius of Truncated Dodecahedron

r m = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot l e

Go Midsphere Radius of Truncated Dodecahedron given Dodecahedral Edge Length

r m = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot \frac{l e(Dodecahedron)}{\sqrt{5}}

Go Midsphere Radius of Truncated Dodecahedron given Total Surface Area

r m = \frac{5 + (3 \cdot \sqrt{5})}{4} \cdot \sqrt{\frac{TSA}{5 \cdot (\sqrt{3} + (6 \cdot \sqrt{5 + (2 \cdot \sqrt{5})}))}}

Go Midsphere Radius of Truncated Dodecahedron given Circumsphere Radius

r m = (5 + (3 \cdot \sqrt{5})) \cdot \frac{r c}{\sqrt{74 + (30 \cdot \sqrt{5})}}

How to Evaluate Midsphere Radius of Truncated Dodecahedron given Volume?

Midsphere Radius of Truncated Dodecahedron given Volume evaluator uses Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3) to evaluate the Midsphere Radius of Truncated Dodecahedron, Midsphere Radius of Truncated Dodecahedron given Volume formula is defined as the radius of the sphere for which all the edges of the Truncated Dodecahedron become a tangent line on that sphere, and calculated using the volume of the Truncated Dodecahedron. Midsphere Radius of Truncated Dodecahedron is denoted by r_m symbol.

How to evaluate Midsphere Radius of Truncated Dodecahedron given Volume using this online evaluator? To use this online evaluator for Midsphere Radius of Truncated Dodecahedron given Volume, enter Volume of Truncated Dodecahedron (V) and hit the calculate button.

FAQs on Midsphere Radius of Truncated Dodecahedron given Volume

What is the formula to find Midsphere Radius of Truncated Dodecahedron given Volume?

The formula of Midsphere Radius of Truncated Dodecahedron given Volume is expressed as Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3). Here is an example- 29.26596 = (5+(3*sqrt(5)))/4*((12*85000)/(5*(99+(47*sqrt(5)))))^(1/3).

How to calculate Midsphere Radius of Truncated Dodecahedron given Volume?

With Volume of Truncated Dodecahedron (V) we can find Midsphere Radius of Truncated Dodecahedron given Volume using the formula - Midsphere Radius of Truncated Dodecahedron = (5+(3*sqrt(5)))/4*((12*Volume of Truncated Dodecahedron)/(5*(99+(47*sqrt(5)))))^(1/3). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Midsphere Radius of Truncated Dodecahedron?

Here are the different ways to Calculate Midsphere Radius of Truncated Dodecahedron-

Midsphere Radius of Truncated Dodecahedron=(5+(3*sqrt(5)))/4*Edge Length of Truncated Dodecahedron
Midsphere Radius of Truncated Dodecahedron=(5+(3*sqrt(5)))/4*Dodecahedral Edge Length of Truncated Dodecahedron/sqrt(5)
Midsphere Radius of Truncated Dodecahedron=(5+(3*sqrt(5)))/4*sqrt(Total Surface Area of Truncated Dodecahedron/(5*(sqrt(3)+(6*sqrt(5+(2*sqrt(5)))))))

Can the Midsphere Radius of Truncated Dodecahedron given Volume be negative?

No, the Midsphere Radius of Truncated Dodecahedron given Volume, measured in Length cannot be negative.

Which unit is used to measure Midsphere Radius of Truncated Dodecahedron given Volume?

Midsphere Radius of Truncated Dodecahedron given Volume 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 Truncated Dodecahedron given Volume can be measured.

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