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Height of Rotunda given Circumsphere Radius Formula

GoHeight of Rotunda Formula

GoHeight of Rotunda given Total Surface Area Formula

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Height of Rotunda is the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda. Check FAQs

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \frac{2 \cdot r c}{1 + \sqrt{5}}

h - Height of Rotunda?r_c - Circumsphere Radius of Rotunda?

Height of Rotunda given Circumsphere Radius Example

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Here is how the Height of Rotunda given Circumsphere Radius equation looks like with Values.

Here is how the Height of Rotunda given Circumsphere Radius equation looks like with Units.

Here is how the Height of Rotunda given Circumsphere Radius equation looks like.

13.6104 = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \frac{2 \cdot 16}{1 + \sqrt{5}}

13.6104m = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \frac{2 \cdot 16m}{1 + \sqrt{5}}

13.6104 = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \frac{2 \cdot 16}{1 + \sqrt{5}}

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Height of Rotunda given Circumsphere Radius Solution

Follow our step by step solution on how to calculate Height of Rotunda given Circumsphere Radius?

FIRST Step Consider the formula

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \frac{2 \cdot r c}{1 + \sqrt{5}}

Next Step Substitute values of Variables

∴

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \frac{2 \cdot 16m}{1 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \frac{2 \cdot 16}{1 + \sqrt{5}}

Next Step Evaluate

∴

h = 13.6104129336326m

LAST Step Rounding Answer

∴

h = 13.6104m

Height of Rotunda given Circumsphere Radius Formula Elements

Variables

Functions

Height of Rotunda

Height of Rotunda is the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Rotunda

Circumsphere Radius of Rotunda

Circumsphere Radius of Rotunda is the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of Rotunda

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 Height of Rotunda

Go Height of Rotunda

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot l e

Go Height of Rotunda given Total Surface Area

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \sqrt{\frac{TSA}{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}}

Go Height of Rotunda given Volume

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot {(\frac{V}{\frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})}^{\frac{1}{3}}

Go Height of Rotunda given Surface to Volume Ratio

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \frac{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}{R A/V \cdot \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))}

How to Evaluate Height of Rotunda given Circumsphere Radius?

Height of Rotunda given Circumsphere Radius evaluator uses Height of Rotunda = sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5)) to evaluate the Height of Rotunda, The Height of Rotunda given Circumsphere Radius formula is defined as the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda and is calculated using the circumsphere radius of the Rotunda. Height of Rotunda is denoted by h symbol.

How to evaluate Height of Rotunda given Circumsphere Radius using this online evaluator? To use this online evaluator for Height of Rotunda given Circumsphere Radius, enter Circumsphere Radius of Rotunda (r_c) and hit the calculate button.

FAQs on Height of Rotunda given Circumsphere Radius

What is the formula to find Height of Rotunda given Circumsphere Radius?

The formula of Height of Rotunda given Circumsphere Radius is expressed as Height of Rotunda = sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5)). Here is an example- 13.61041 = sqrt(1+2/sqrt(5))*(2*16)/(1+sqrt(5)).

How to calculate Height of Rotunda given Circumsphere Radius?

With Circumsphere Radius of Rotunda (r_c) we can find Height of Rotunda given Circumsphere Radius using the formula - Height of Rotunda = sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Height of Rotunda?

Here are the different ways to Calculate Height of Rotunda-

Height of Rotunda=sqrt(1+2/sqrt(5))*Edge Length of Rotunda
Height of Rotunda=sqrt(1+2/sqrt(5))*sqrt(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))))
Height of Rotunda=sqrt(1+2/sqrt(5))*(Volume of Rotunda/(1/12*(45+(17*sqrt(5)))))^(1/3)

Can the Height of Rotunda given Circumsphere Radius be negative?

No, the Height of Rotunda given Circumsphere Radius, measured in Length cannot be negative.

Which unit is used to measure Height of Rotunda given Circumsphere Radius?

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

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