Volume of Rotunda given Circumsphere Radius Calculator

✖Circumsphere Radius of Rotunda is the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere.ⓘ Circumsphere Radius of Rotunda [r_c]

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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 given Circumsphere Radius [V]

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Volume of Rotunda given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*((2*Circumsphere Radius of Rotunda)/(1+sqrt(5)))^3
V = 1/12*(45+(17*sqrt(5)))*((2*r_c)/(1+sqrt(5)))^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.
Circumsphere Radius of Rotunda - (Measured in Meter) - Circumsphere Radius of Rotunda is the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere.

STEP 1: Convert Input(s) to Base Unit

Circumsphere Radius of Rotunda: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 1/12*(45+(17*sqrt(5)))*((2*r_c)/(1+sqrt(5)))^3 --> 1/12*(45+(17*sqrt(5)))*((2*16)/(1+sqrt(5)))^3

Evaluating ... ...

V = 6689.02323285254

STEP 3: Convert Result to Output's Unit

6689.02323285254 Cubic Meter --> No Conversion Required

FINAL ANSWER

6689.02323285254 ≈ 6689.023 Cubic Meter <-- Volume of Rotunda

(Calculation completed in 00.004 seconds)

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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 given Circumsphere Radius Formula

LaTeX Go

Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*((2*Circumsphere Radius of Rotunda)/(1+sqrt(5)))^3
V = 1/12*(45+(17*sqrt(5)))*((2*r_c)/(1+sqrt(5)))^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 given Circumsphere Radius?

Volume of Rotunda given Circumsphere Radius calculator uses Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*((2*Circumsphere Radius of Rotunda)/(1+sqrt(5)))^3 to calculate the Volume of Rotunda, The Volume of Rotunda given Circumsphere Radius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Rotunda and is calculated using the circumsphere radius of the Rotunda. Volume of Rotunda is denoted by V symbol.

How to calculate Volume of Rotunda given Circumsphere Radius using this online calculator? To use this online calculator for Volume of Rotunda given Circumsphere Radius, enter Circumsphere Radius of Rotunda (r_c) and hit the calculate button. Here is how the Volume of Rotunda given Circumsphere Radius calculation can be explained with given input values -> 6689.023 = 1/12*(45+(17*sqrt(5)))*((2*16)/(1+sqrt(5)))^3.

FAQ

What is Volume of Rotunda given Circumsphere Radius?

The Volume of Rotunda given Circumsphere Radius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Rotunda and is calculated using the circumsphere radius of the Rotunda and is represented as V = 1/12*(45+(17*sqrt(5)))*((2*r_c)/(1+sqrt(5)))^3 or Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*((2*Circumsphere Radius of Rotunda)/(1+sqrt(5)))^3. Circumsphere Radius of Rotunda is the radius of the sphere that contains the Rotunda in such a way that all the vertices of the Rotunda are touching the sphere.

How to calculate Volume of Rotunda given Circumsphere Radius?

The Volume of Rotunda given Circumsphere Radius formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Rotunda and is calculated using the circumsphere radius of the Rotunda is calculated using Volume of Rotunda = 1/12*(45+(17*sqrt(5)))*((2*Circumsphere Radius of Rotunda)/(1+sqrt(5)))^3. To calculate Volume of Rotunda given Circumsphere Radius, you need Circumsphere Radius of Rotunda (r_c). With our tool, you need to enter the respective value for Circumsphere Radius 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 Circumsphere Radius 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)))*Edge Length of Rotunda^3
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)

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