Surface to Volume Ratio of Pentagonal Cupola given Height Calculator

✖Height of Pentagonal Cupola is the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola.ⓘ Height of Pentagonal Cupola [h]

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✖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 given Height [R_A/V]

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Formula

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Surface to Volume Ratio of Pentagonal Cupola given Height

Formula

`"R"_{"A/V"} = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*("h"/sqrt(1-(1/4*cosec(pi/5)^(2)))))`

Example

`"0.750114m⁻¹"=(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*("5m"/sqrt(1-(1/4*cosec(pi/5)^(2)))))`

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Surface to Volume Ratio of Pentagonal Cupola given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Pentagonal Cupola = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2)))))
R_A/V = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(h/sqrt(1-(1/4*cosec(pi/5)^(2)))))
This formula uses 1 Constants, 3 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
cosec - The cosecant function is a trigonometric function that is the reciprocal of the sine function., cosec(Angle)
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

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.
Height of Pentagonal Cupola - (Measured in Meter) - Height of Pentagonal Cupola is the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola.

STEP 1: Convert Input(s) to Base Unit

Height of Pentagonal Cupola: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(h/sqrt(1-(1/4*cosec(pi/5)^(2))))) --> (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(5/sqrt(1-(1/4*cosec(pi/5)^(2)))))

Evaluating ... ...

R_A/V = 0.750113623648861

STEP 3: Convert Result to Output's Unit

0.750113623648861 1 per Meter --> No Conversion Required

FINAL ANSWER

0.750113623648861 ≈ 0.750114 1 per Meter <-- Surface to Volume Ratio of Pentagonal Cupola

(Calculation completed in 00.004 seconds)

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< 4 Surface to Volume Ratio of Pentagonal Cupola Calculators

Surface to Volume Ratio of Pentagonal Cupola given Total Surface Area

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

Surface to Volume Ratio of Pentagonal Cupola given Height

Go Surface to Volume Ratio of Pentagonal Cupola = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2)))))

Surface to Volume Ratio of Pentagonal Cupola given Volume

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

Surface to Volume Ratio of Pentagonal Cupola

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

Surface to Volume Ratio of Pentagonal Cupola given Height 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 Surface to Volume Ratio of Pentagonal Cupola given Height?

Surface to Volume Ratio of Pentagonal Cupola given Height calculator uses Surface to Volume Ratio of Pentagonal Cupola = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))) to calculate the Surface to Volume Ratio of Pentagonal Cupola, The Surface to Volume Ratio of Pentagonal Cupola given Height formula is defined as the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola and is calculated using the height of the Pentagonal Cupola. Surface to Volume Ratio of Pentagonal Cupola is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Pentagonal Cupola given Height using this online calculator? To use this online calculator for Surface to Volume Ratio of Pentagonal Cupola given Height, enter Height of Pentagonal Cupola (h) and hit the calculate button. Here is how the Surface to Volume Ratio of Pentagonal Cupola given Height calculation can be explained with given input values -> 0.750114 = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(5/sqrt(1-(1/4*cosec(pi/5)^(2))))).

FAQ

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

The Surface to Volume Ratio of Pentagonal Cupola given Height formula is defined as the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola and is calculated using the height of the Pentagonal Cupola and is represented as R_A/V = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(h/sqrt(1-(1/4*cosec(pi/5)^(2))))) or Surface to Volume Ratio of Pentagonal Cupola = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))). Height of Pentagonal Cupola is the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola.

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

The Surface to Volume Ratio of Pentagonal Cupola given Height formula is defined as the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola and is calculated using the height of the Pentagonal Cupola is calculated using Surface to Volume Ratio of Pentagonal Cupola = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))). To calculate Surface to Volume Ratio of Pentagonal Cupola given Height, you need Height of Pentagonal Cupola (h). With our tool, you need to enter the respective value for Height 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 Surface to Volume Ratio of Pentagonal Cupola?

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

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

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