Surface to Volume Ratio of Square Cupola given Height Calculator

✖Height of Square Cupola is the vertical distance from the square face to the opposite octagonal face of the Square Cupola.ⓘ Height of Square Cupola [h]

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

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Surface to Volume Ratio of Square Cupola given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(2)))))
R_A/V = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(h/sqrt(1-(1/4*cosec(pi/4)^(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 Square Cupola - (Measured in 1 per Meter) - Surface to Volume Ratio of Square Cupola is the numerical ratio of the total surface area of a Square Cupola to the volume of the Square Cupola.
Height of Square Cupola - (Measured in Meter) - Height of Square Cupola is the vertical distance from the square face to the opposite octagonal face of the Square Cupola.

STEP 1: Convert Input(s) to Base Unit

Height of Square Cupola: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(h/sqrt(1-(1/4*cosec(pi/4)^(2))))) --> (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(7/sqrt(1-(1/4*cosec(pi/4)^(2)))))

Evaluating ... ...

R_A/V = 0.601080494769484

STEP 3: Convert Result to Output's Unit

0.601080494769484 1 per Meter --> No Conversion Required

FINAL ANSWER

0.601080494769484 ≈ 0.60108 1 per Meter <-- Surface to Volume Ratio of Square Cupola

(Calculation completed in 00.007 seconds)

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< Surface to Volume Ratio of Square Cupola Calculators

Surface to Volume Ratio of Square Cupola given Total Surface Area

LaTeX Go Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3))))

Surface to Volume Ratio of Square Cupola given Height

LaTeX Go Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(2)))))

Surface to Volume Ratio of Square Cupola given Volume

LaTeX Go Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3))

Surface to Volume Ratio of Square Cupola

LaTeX Go Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*Edge Length of Square Cupola)

Surface to Volume Ratio of Square Cupola given Height Formula

LaTeX Go

What is a Square 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 Square Cupola has 10 faces, 20 edges, and 12 vertices. Its top surface is a square and the base surface is a regular octagon.

How to Calculate Surface to Volume Ratio of Square Cupola given Height?

Surface to Volume Ratio of Square Cupola given Height calculator uses Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(2))))) to calculate the Surface to Volume Ratio of Square Cupola, The Surface to Volume Ratio of Square Cupola given Height formula is defined as the numerical ratio of the total surface area of a Square Cupola to the volume of the Square Cupola and is calculated using the height of the Square Cupola. Surface to Volume Ratio of Square Cupola is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Square Cupola given Height using this online calculator? To use this online calculator for Surface to Volume Ratio of Square Cupola given Height, enter Height of Square Cupola (h) and hit the calculate button. Here is how the Surface to Volume Ratio of Square Cupola given Height calculation can be explained with given input values -> 0.60108 = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(7/sqrt(1-(1/4*cosec(pi/4)^(2))))).

FAQ

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

The Surface to Volume Ratio of Square Cupola given Height formula is defined as the numerical ratio of the total surface area of a Square Cupola to the volume of the Square Cupola and is calculated using the height of the Square Cupola and is represented as R_A/V = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(h/sqrt(1-(1/4*cosec(pi/4)^(2))))) or Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(2))))). Height of Square Cupola is the vertical distance from the square face to the opposite octagonal face of the Square Cupola.

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

The Surface to Volume Ratio of Square Cupola given Height formula is defined as the numerical ratio of the total surface area of a Square Cupola to the volume of the Square Cupola and is calculated using the height of the Square Cupola is calculated using Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(2))))). To calculate Surface to Volume Ratio of Square Cupola given Height, you need Height of Square Cupola (h). With our tool, you need to enter the respective value for Height of Square 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 Square Cupola?

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

Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*Edge Length of Square Cupola)
Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3))))
Surface to Volume Ratio of Square Cupola = (7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*(Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3))

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