Height of Rotunda given Circumsphere Radius Calculator

✖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.ⓘ Circumsphere Radius of Rotunda [r_c]

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✖Height of Rotunda is the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda.ⓘ Height of Rotunda given Circumsphere Radius [h]

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Height of Rotunda given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Rotunda = sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5))
h = sqrt(1+2/sqrt(5))*(2*r_c)/(1+sqrt(5))
This formula uses 1 Functions, 2 Variables

Functions Used

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., sqrt(Number)

Variables Used

Height of Rotunda - (Measured in Meter) - Height of Rotunda is the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda.
Circumsphere Radius of Rotunda - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Rotunda: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(1+2/sqrt(5))*(2*r_c)/(1+sqrt(5)) --> sqrt(1+2/sqrt(5))*(2*16)/(1+sqrt(5))

Evaluating ... ...

h = 13.6104129336326

STEP 3: Convert Result to Output's Unit

13.6104129336326 Meter --> No Conversion Required

FINAL ANSWER

13.6104129336326 ≈ 13.61041 Meter <-- Height of Rotunda

(Calculation completed in 00.004 seconds)

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< Height of Rotunda Calculators

Height of Rotunda given Total Surface Area

LaTeX Go 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 given Volume

LaTeX Go Height of Rotunda = sqrt(1+2/sqrt(5))*(Volume of Rotunda/(1/12*(45+(17*sqrt(5)))))^(1/3)

Height of Rotunda given Circumsphere Radius

LaTeX Go Height of Rotunda = sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5))

Height of Rotunda

LaTeX Go Height of Rotunda = sqrt(1+2/sqrt(5))*Edge Length of Rotunda

Height of Rotunda given Circumsphere Radius Formula

LaTeX Go

Height of Rotunda = sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5))
h = sqrt(1+2/sqrt(5))*(2*r_c)/(1+sqrt(5))

What is a Rotunda?

A Rotunda is similar to a cupola but has pentagons instead of quadrangles as side faces. The regular pentagonal rotunda is Johnson solid which is generally denoted by J6. It has 17 faces which include a regular pentagonal face at the top, a regular decagonal face at the bottom, 10 equilateral triangular faces, and 5 regular pentagonal faces. Also, It has 35 edges and 20 vertices.

How to Calculate Height of Rotunda given Circumsphere Radius?

Height of Rotunda given Circumsphere Radius calculator uses Height of Rotunda = sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5)) to calculate 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 calculate Height of Rotunda given Circumsphere Radius using this online calculator? To use this online calculator for Height of Rotunda given Circumsphere Radius, enter Circumsphere Radius of Rotunda (r_c) and hit the calculate button. Here is how the Height of Rotunda given Circumsphere Radius calculation can be explained with given input values -> 13.61041 = sqrt(1+2/sqrt(5))*(2*16)/(1+sqrt(5)).

FAQ

What is Height of Rotunda given Circumsphere Radius?

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 and is represented as h = sqrt(1+2/sqrt(5))*(2*r_c)/(1+sqrt(5)) or Height of Rotunda = sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5)). 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.

How to calculate Height of Rotunda given Circumsphere Radius?

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 is calculated using Height of Rotunda = sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5)). To calculate Height of Rotunda given Circumsphere Radius, you need Circumsphere Radius of Rotunda (r_c). With our tool, you need to enter the respective value for Circumsphere Radius of Rotunda and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Height of Rotunda?

In this formula, Height of Rotunda uses Circumsphere Radius of Rotunda. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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