Height 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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✖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 given Surface to Volume Ratio [h]

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Formula

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Height of Pentagonal Cupola given Surface to Volume Ratio

Formula

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

Example

`"5.357954m"=(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*"0.7m⁻¹")*sqrt(1-(1/4*cosec(pi/5)^(2)))`

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Height of Pentagonal Cupola given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

h = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*R_A/V)*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)))*0.7)*sqrt(1-(1/4*cosec(pi/5)^(2)))

Evaluating ... ...

h = 5.35795445463472

STEP 3: Convert Result to Output's Unit

5.35795445463472 Meter --> No Conversion Required

FINAL ANSWER

5.35795445463472 ≈ 5.357954 Meter <-- Height of Pentagonal Cupola

(Calculation completed in 00.004 seconds)

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< 4 Height of Pentagonal Cupola Calculators

Height of Pentagonal Cupola given Surface to Volume Ratio

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

Height of Pentagonal Cupola given Total Surface Area

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

Height of Pentagonal Cupola given Volume

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

Height of Pentagonal Cupola

Go Height of Pentagonal Cupola = Edge Length of Pentagonal Cupola*sqrt(1-(1/4*cosec(pi/5)^(2)))

Height 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 Height of Pentagonal Cupola given Surface to Volume Ratio?

Height of Pentagonal Cupola given Surface to Volume Ratio calculator uses Height of Pentagonal Cupola = (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)*sqrt(1-(1/4*cosec(pi/5)^(2))) to calculate the Height of Pentagonal Cupola, The Height of Pentagonal Cupola given Surface to Volume Ratio formula is defined as the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola and is calculated using the surface to volume ratio of the Pentagonal Cupola. Height of Pentagonal Cupola is denoted by h symbol.

How to calculate Height of Pentagonal Cupola given Surface to Volume Ratio using this online calculator? To use this online calculator for Height 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 Height of Pentagonal Cupola given Surface to Volume Ratio calculation can be explained with given input values -> 5.357954 = (1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*0.7)*sqrt(1-(1/4*cosec(pi/5)^(2))).

FAQ

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

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

The Height of Pentagonal Cupola given Surface to Volume Ratio formula is defined as the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola and is calculated using the surface to volume ratio of the Pentagonal Cupola is calculated using Height of Pentagonal Cupola = (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)*sqrt(1-(1/4*cosec(pi/5)^(2))). To calculate Height 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 Height of Pentagonal Cupola?

In this formula, Height 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 -

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

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