Volume of Triangular Cupola given Surface to Volume Ratio Calculator

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

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

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Formula

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Volume of Triangular Cupola given Surface to Volume Ratio

Formula

`"V" = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*"R"_{"A/V"}))^(3)`

Example

`"1312.844m³"=5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*"0.6m⁻¹"))^(3)`

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Volume of Triangular Cupola given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Triangular Cupola = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola))^(3)
V = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(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 Triangular Cupola - (Measured in Cubic Meter) - Volume of Triangular Cupola is the total quantity of three-dimensional space enclosed by the surface of the Triangular Cupola.
Surface to Volume Ratio of Triangular Cupola - (Measured in 1 per Meter) - Surface to Volume Ratio of Triangular Cupola is the numerical ratio of the total surface area of a Triangular Cupola to the volume of the Triangular Cupola.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Triangular Cupola: 0.6 1 per Meter --> 0.6 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*R_A/V))^(3) --> 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*0.6))^(3)

Evaluating ... ...

V = 1312.84437038563

STEP 3: Convert Result to Output's Unit

1312.84437038563 Cubic Meter --> No Conversion Required

FINAL ANSWER

1312.84437038563 ≈ 1312.844 Cubic Meter <-- Volume of Triangular Cupola

(Calculation completed in 00.004 seconds)

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< 4 Volume of Triangular Cupola Calculators

Volume of Triangular Cupola given Height

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

Volume of Triangular Cupola given Surface to Volume Ratio

Go Volume of Triangular Cupola = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola))^(3)

Volume of Triangular Cupola given Total Surface Area

Go Volume of Triangular Cupola = 5/(3*sqrt(2))*(Total Surface Area of Triangular Cupola/(3+(5*sqrt(3))/2))^(3/2)

Volume of Triangular Cupola

Go Volume of Triangular Cupola = 5/(3*sqrt(2))*Edge Length of Triangular Cupola^(3)

Volume of Triangular Cupola given Surface to Volume Ratio Formula

Volume of Triangular Cupola = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola))^(3)
V = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*R_A/V))^(3)

What is a Triangular 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 Triangular Cupola has 8 faces, 15 edges, and 9 vertices. Its top surface is an equilateral triangle and its base surface is a regular hexagon.

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

Volume of Triangular Cupola given Surface to Volume Ratio calculator uses Volume of Triangular Cupola = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola))^(3) to calculate the Volume of Triangular Cupola, The Volume of Triangular Cupola given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Triangular Cupola and is calculated using the surface to volume ratio of the Triangular Cupola. Volume of Triangular Cupola is denoted by V symbol.

How to calculate Volume of Triangular Cupola given Surface to Volume Ratio using this online calculator? To use this online calculator for Volume of Triangular Cupola given Surface to Volume Ratio, enter Surface to Volume Ratio of Triangular Cupola (R_A/V) and hit the calculate button. Here is how the Volume of Triangular Cupola given Surface to Volume Ratio calculation can be explained with given input values -> 1312.844 = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*0.6))^(3).

FAQ

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

The Volume of Triangular Cupola given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Triangular Cupola and is calculated using the surface to volume ratio of the Triangular Cupola and is represented as V = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*R_A/V))^(3) or Volume of Triangular Cupola = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola))^(3). Surface to Volume Ratio of Triangular Cupola is the numerical ratio of the total surface area of a Triangular Cupola to the volume of the Triangular Cupola.

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

The Volume of Triangular Cupola given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Triangular Cupola and is calculated using the surface to volume ratio of the Triangular Cupola is calculated using Volume of Triangular Cupola = 5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola))^(3). To calculate Volume of Triangular Cupola given Surface to Volume Ratio, you need Surface to Volume Ratio of Triangular Cupola (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Triangular 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 Triangular Cupola?

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

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

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