Height of Rotunda Calculator

✖Edge Length of Rotunda is the length of any edge of the Rotunda.ⓘ Edge Length of Rotunda [l_e]

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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 [h]

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Height of Rotunda Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Rotunda = sqrt(1+2/sqrt(5))*Edge Length of Rotunda
h = sqrt(1+2/sqrt(5))*l_e
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.
Edge Length of Rotunda - (Measured in Meter) - Edge Length of Rotunda is the length of any edge of the Rotunda.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Rotunda: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(1+2/sqrt(5))*l_e --> sqrt(1+2/sqrt(5))*10

Evaluating ... ...

h = 13.7638192047117

STEP 3: Convert Result to Output's Unit

13.7638192047117 Meter --> No Conversion Required

FINAL ANSWER

13.7638192047117 ≈ 13.76382 Meter <-- Height of Rotunda

(Calculation completed in 00.006 seconds)

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Credits

Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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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 Formula

LaTeX Go

Height of Rotunda = sqrt(1+2/sqrt(5))*Edge Length of Rotunda
h = sqrt(1+2/sqrt(5))*l_e

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?

Height of Rotunda calculator uses Height of Rotunda = sqrt(1+2/sqrt(5))*Edge Length of Rotunda to calculate the Height of Rotunda, The Height of Rotunda formula is defined as the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda. Height of Rotunda is denoted by h symbol.

How to calculate Height of Rotunda using this online calculator? To use this online calculator for Height of Rotunda, enter Edge Length of Rotunda (l_e) and hit the calculate button. Here is how the Height of Rotunda calculation can be explained with given input values -> 13.76382 = sqrt(1+2/sqrt(5))*10.

FAQ

What is Height of Rotunda?

The Height of Rotunda formula is defined as the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda and is represented as h = sqrt(1+2/sqrt(5))*l_e or Height of Rotunda = sqrt(1+2/sqrt(5))*Edge Length of Rotunda. Edge Length of Rotunda is the length of any edge of the Rotunda.

How to calculate Height of Rotunda?

The Height of Rotunda formula is defined as the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda is calculated using Height of Rotunda = sqrt(1+2/sqrt(5))*Edge Length of Rotunda. To calculate Height of Rotunda, you need Edge Length of Rotunda (l_e). With our tool, you need to enter the respective value for Edge Length 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 Edge Length 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))*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)
Height of Rotunda = sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5))

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