Edge Length of Rotunda given Height Calculator

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

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Edge Length of Rotunda given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Edge Length of Rotunda - (Measured in Meter) - Edge Length of Rotunda is the length of any edge of the Rotunda.
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.

STEP 1: Convert Input(s) to Base Unit

Height of Rotunda: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = h/(sqrt(1+2/sqrt(5))) --> 14/(sqrt(1+2/sqrt(5)))

Evaluating ... ...

l_e = 10.1715953920751

STEP 3: Convert Result to Output's Unit

10.1715953920751 Meter --> No Conversion Required

FINAL ANSWER

10.1715953920751 ≈ 10.1716 Meter <-- Edge Length of Rotunda

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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< Edge Length of Rotunda Calculators

Edge Length of Rotunda given Total Surface Area

LaTeX Go Edge Length of Rotunda = sqrt(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))))

Edge Length of Rotunda given Height

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

Edge Length of Rotunda given Volume

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

Edge Length of Rotunda given Circumsphere Radius

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

Edge Length of Rotunda given Height Formula

LaTeX Go

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

Edge Length of Rotunda given Height calculator uses Edge Length of Rotunda = Height of Rotunda/(sqrt(1+2/sqrt(5))) to calculate the Edge Length of Rotunda, The Edge Length of Rotunda given Height formula is defined as the length of any edge of the Rotunda and is calculated using the height of the Rotunda. Edge Length of Rotunda is denoted by l_e symbol.

How to calculate Edge Length of Rotunda given Height using this online calculator? To use this online calculator for Edge Length of Rotunda given Height, enter Height of Rotunda (h) and hit the calculate button. Here is how the Edge Length of Rotunda given Height calculation can be explained with given input values -> 10.1716 = 14/(sqrt(1+2/sqrt(5))).

FAQ

What is Edge Length of Rotunda given Height?

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

How to calculate Edge Length of Rotunda given Height?

The Edge Length of Rotunda given Height formula is defined as the length of any edge of the Rotunda and is calculated using the height of the Rotunda is calculated using Edge Length of Rotunda = Height of Rotunda/(sqrt(1+2/sqrt(5))). To calculate Edge Length of Rotunda given Height, you need Height of Rotunda (h). With our tool, you need to enter the respective value for Height 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 Edge Length of Rotunda?

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

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

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