Total Surface Area of Rotunda given Volume Calculator

✖Volume of Rotunda is the total quantity of three-dimensional space enclosed by the surface of the Rotunda.ⓘ Volume of Rotunda [V]

+10%

-10%

✖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 Volume [TSA]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Johnson Solids Formula PDF PDF Image

Total Surface Area of Rotunda given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
TSA = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(V/(1/12*(45+(17*sqrt(5)))))^(2/3)
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.
Volume of Rotunda - (Measured in Cubic Meter) - Volume of Rotunda is the total quantity of three-dimensional space enclosed by the surface of the Rotunda.

STEP 1: Convert Input(s) to Base Unit

Volume of Rotunda: 7000 Cubic Meter --> 7000 Cubic 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)))))*(V/(1/12*(45+(17*sqrt(5)))))^(2/3) --> 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(7000/(1/12*(45+(17*sqrt(5)))))^(2/3)

Evaluating ... ...

TSA = 2252.39573436467

STEP 3: Convert Result to Output's Unit

2252.39573436467 Square Meter --> No Conversion Required

FINAL ANSWER

2252.39573436467 ≈ 2252.396 Square Meter <-- Total Surface Area of Rotunda

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Johnson Solids » Rotunda » Surface Area of Rotunda » Total Surface Area of Rotunda given Volume

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

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< 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 Volume Formula

LaTeX Go

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 Volume?

Total Surface Area of Rotunda given Volume calculator uses 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) to calculate the Total Surface Area of Rotunda, The Total Surface Area of Rotunda given Volume formula is defined as the total amount of two-dimensional space occupied by all the faces of the Rotunda and is calculated using the volume of the Rotunda. Total Surface Area of Rotunda is denoted by TSA symbol.

How to calculate Total Surface Area of Rotunda given Volume using this online calculator? To use this online calculator for Total Surface Area of Rotunda given Volume, enter Volume of Rotunda (V) and hit the calculate button. Here is how the Total Surface Area of Rotunda given Volume calculation can be explained with given input values -> 2252.396 = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(7000/(1/12*(45+(17*sqrt(5)))))^(2/3).

FAQ

What is Total Surface Area of Rotunda given Volume?

The Total Surface Area of Rotunda given Volume formula is defined as the total amount of two-dimensional space occupied by all the faces of the Rotunda and is calculated using the volume of the Rotunda and is represented as TSA = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(V/(1/12*(45+(17*sqrt(5)))))^(2/3) or 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). Volume of Rotunda is the total quantity of three-dimensional space enclosed by the surface of the Rotunda.

How to calculate Total Surface Area of Rotunda given Volume?

The Total Surface Area of Rotunda given Volume formula is defined as the total amount of two-dimensional space occupied by all the faces of the Rotunda and is calculated using the volume of the Rotunda is calculated using 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). To calculate Total Surface Area of Rotunda given Volume, you need Volume of Rotunda (V). With our tool, you need to enter the respective value for Volume 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 Volume 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)))))*(Height of Rotunda/(sqrt(1+2/sqrt(5))))^2
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

Home

FREE PDFs

🔍 Search