Total Surface Area 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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✖Total Surface Area of Rotunda is the total amount of two-dimensional space occupied by all the faces of the Rotunda.ⓘ Total Surface Area of Rotunda given Height [TSA]

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Total Surface Area of Rotunda given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Rotunda = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(Height of Rotunda/(sqrt(1+2/sqrt(5))))^2
TSA = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(h/(sqrt(1+2/sqrt(5))))^2
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

Total Surface Area of Rotunda - (Measured in Square Meter) - Total Surface Area of Rotunda is the total amount of two-dimensional space occupied by all the faces 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

TSA = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(h/(sqrt(1+2/sqrt(5))))^2 --> 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(14/(sqrt(1+2/sqrt(5))))^2

Evaluating ... ...

TSA = 2312.07157119898

STEP 3: Convert Result to Output's Unit

2312.07157119898 Square Meter --> No Conversion Required

FINAL ANSWER

2312.07157119898 ≈ 2312.072 Square Meter <-- Total Surface Area of Rotunda

(Calculation completed in 00.004 seconds)

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< Surface Area of Rotunda Calculators

Total Surface Area of Rotunda given Height

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

Total Surface Area of Rotunda given Circumsphere Radius

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

Total Surface Area of Rotunda given Volume

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

Total Surface Area of Rotunda

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

Total Surface Area of Rotunda given Height Formula

LaTeX Go

Total Surface Area of Rotunda = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(Height of Rotunda/(sqrt(1+2/sqrt(5))))^2
TSA = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(h/(sqrt(1+2/sqrt(5))))^2

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 Total Surface Area of Rotunda given Height?

Total Surface Area of Rotunda given Height calculator uses Total Surface Area of Rotunda = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(Height of Rotunda/(sqrt(1+2/sqrt(5))))^2 to calculate the Total Surface Area of Rotunda, The Total Surface Area of Rotunda given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Rotunda and is calculated using the height of the Rotunda. Total Surface Area of Rotunda is denoted by TSA symbol.

How to calculate Total Surface Area of Rotunda given Height using this online calculator? To use this online calculator for Total Surface Area of Rotunda given Height, enter Height of Rotunda (h) and hit the calculate button. Here is how the Total Surface Area of Rotunda given Height calculation can be explained with given input values -> 2312.072 = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(14/(sqrt(1+2/sqrt(5))))^2.

FAQ

What is Total Surface Area of Rotunda given Height?

The Total Surface Area of Rotunda given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Rotunda and is calculated using the height of the Rotunda and is represented as TSA = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(h/(sqrt(1+2/sqrt(5))))^2 or Total Surface Area of Rotunda = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(Height of Rotunda/(sqrt(1+2/sqrt(5))))^2. Height of Rotunda is the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda.

How to calculate Total Surface Area of Rotunda given Height?

The Total Surface Area of Rotunda given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Rotunda and is calculated using the height of the Rotunda is calculated using Total Surface Area of Rotunda = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(Height of Rotunda/(sqrt(1+2/sqrt(5))))^2. To calculate Total Surface Area 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 Total Surface Area of Rotunda?

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

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

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