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

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Volume of Rotunda Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

V = 1/12*(45+(17*sqrt(5)))*l_e^3 --> 1/12*(45+(17*sqrt(5)))*10^3

Evaluating ... ...

V = 6917.7629681247

STEP 3: Convert Result to Output's Unit

6917.7629681247 Cubic Meter --> No Conversion Required

FINAL ANSWER

6917.7629681247 ≈ 6917.763 Cubic Meter <-- Volume of Rotunda

(Calculation completed in 00.008 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Indian Institute of Information Technology (IIIT), Bhopal

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< Volume of Rotunda Calculators

Volume of Rotunda given Total Surface Area

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

Volume of Rotunda given Height

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

Volume of Rotunda given Circumsphere Radius

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

Volume of Rotunda

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

Volume of Rotunda Formula

LaTeX Go

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

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 Volume of Rotunda?

Volume of Rotunda calculator uses Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*Edge Length of Rotunda^3 to calculate the Volume of Rotunda, The Volume of Rotunda formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Rotunda. Volume of Rotunda is denoted by V symbol.

How to calculate Volume of Rotunda using this online calculator? To use this online calculator for Volume of Rotunda, enter Edge Length of Rotunda (l_e) and hit the calculate button. Here is how the Volume of Rotunda calculation can be explained with given input values -> 6917.763 = 1/12*(45+(17*sqrt(5)))*10^3.

FAQ

What is Volume of Rotunda?

The Volume of Rotunda formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Rotunda and is represented as V = 1/12*(45+(17*sqrt(5)))*l_e^3 or Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*Edge Length of Rotunda^3. Edge Length of Rotunda is the length of any edge of the Rotunda.

How to calculate Volume of Rotunda?

The Volume of Rotunda formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Rotunda is calculated using Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*Edge Length of Rotunda^3. To calculate Volume 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 Volume of Rotunda?

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

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

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