Volume of Pentagonal Cupola given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Pentagonal Cupola is the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola.ⓘ Surface to Volume Ratio of Pentagonal Cupola [R_A/V]

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✖Volume of Pentagonal Cupola is the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola.ⓘ Volume of Pentagonal Cupola given Surface to Volume Ratio [V]

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Formula

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Volume of Pentagonal Cupola given Surface to Volume Ratio

Formula

`"V" = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*"R"_{"A/V"}))^3`

Example

`"2460.088m³"=1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*"0.7m⁻¹"))^3`

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Volume of Pentagonal Cupola given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Surface to Volume Ratio of Pentagonal Cupola))^3
V = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*R_A/V))^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 Pentagonal Cupola - (Measured in Cubic Meter) - Volume of Pentagonal Cupola is the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola.
Surface to Volume Ratio of Pentagonal Cupola - (Measured in 1 per Meter) - Surface to Volume Ratio of Pentagonal Cupola is the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Pentagonal Cupola: 0.7 1 per Meter --> 0.7 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*R_A/V))^3 --> 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*0.7))^3

Evaluating ... ...

V = 2460.08780847747

STEP 3: Convert Result to Output's Unit

2460.08780847747 Cubic Meter --> No Conversion Required

FINAL ANSWER

2460.08780847747 ≈ 2460.088 Cubic Meter <-- Volume of Pentagonal Cupola

(Calculation completed in 00.004 seconds)

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< 4 Volume of Pentagonal Cupola Calculators

Volume of Pentagonal Cupola given Surface to Volume Ratio

Go Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Surface to Volume Ratio of Pentagonal Cupola))^3

Volume of Pentagonal Cupola given Total Surface Area

Go Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Total Surface Area of Pentagonal Cupola/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))))^(3/2)

Volume of Pentagonal Cupola given Height

Go Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))^3

Volume of Pentagonal Cupola

Go Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*Edge Length of Pentagonal Cupola^3

Volume of Pentagonal Cupola given Surface to Volume Ratio Formula

What is a Pentagonal Cupola?

A cupola is a polyhedron with two opposite polygons, of which one has twice as many vertices as the other and with alternating triangles and quadrangles as side faces. When all faces of the cupola are regular, then the cupola itself is regular and is a Johnson solid. There are three regular cupolae, the triangular, the square, and the pentagonal cupola. A Pentagonal Cupola has 12 faces, 25 edges, and 15 vertices. Its top surface is a regular pentagon and the base surface is a regular decagon.

How to Calculate Volume of Pentagonal Cupola given Surface to Volume Ratio?

Volume of Pentagonal Cupola given Surface to Volume Ratio calculator uses Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Surface to Volume Ratio of Pentagonal Cupola))^3 to calculate the Volume of Pentagonal Cupola, The Volume of Pentagonal Cupola given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola and is calculated using the surface to volume ratio of the Pentagonal Cupola. Volume of Pentagonal Cupola is denoted by V symbol.

How to calculate Volume of Pentagonal Cupola given Surface to Volume Ratio using this online calculator? To use this online calculator for Volume of Pentagonal Cupola given Surface to Volume Ratio, enter Surface to Volume Ratio of Pentagonal Cupola (R_A/V) and hit the calculate button. Here is how the Volume of Pentagonal Cupola given Surface to Volume Ratio calculation can be explained with given input values -> 2460.088 = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*0.7))^3.

FAQ

What is Volume of Pentagonal Cupola given Surface to Volume Ratio?

The Volume of Pentagonal Cupola given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola and is calculated using the surface to volume ratio of the Pentagonal Cupola and is represented as V = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*R_A/V))^3 or Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Surface to Volume Ratio of Pentagonal Cupola))^3. Surface to Volume Ratio of Pentagonal Cupola is the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola.

How to calculate Volume of Pentagonal Cupola given Surface to Volume Ratio?

The Volume of Pentagonal Cupola given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola and is calculated using the surface to volume ratio of the Pentagonal Cupola is calculated using Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Surface to Volume Ratio of Pentagonal Cupola))^3. To calculate Volume of Pentagonal Cupola given Surface to Volume Ratio, you need Surface to Volume Ratio of Pentagonal Cupola (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Pentagonal Cupola 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 Pentagonal Cupola?

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

Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*Edge Length of Pentagonal Cupola^3
Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))^3
Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Total Surface Area of Pentagonal Cupola/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))))^(3/2)

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