Total Surface Area 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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✖Total Surface Area of Pentagonal Cupola is the total amount of 2D space occupied by all the faces of the Pentagonal Cupola.ⓘ Total Surface Area of Pentagonal Cupola given Height [TSA]

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Total Surface Area of Pentagonal Cupola given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Total Surface Area of Pentagonal Cupola - (Measured in Square Meter) - Total Surface Area of Pentagonal Cupola is the total amount of 2D space occupied by all the faces 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

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

Evaluating ... ...

TSA = 1499.65245328197

STEP 3: Convert Result to Output's Unit

1499.65245328197 Square Meter --> No Conversion Required

FINAL ANSWER

1499.65245328197 ≈ 1499.652 Square Meter <-- Total Surface Area of Pentagonal Cupola

(Calculation completed in 00.004 seconds)

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< Total Surface Area of Pentagonal Cupola Calculators

Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio

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

Total Surface Area of Pentagonal Cupola given Height

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

Total Surface Area of Pentagonal Cupola given Volume

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

Total Surface Area of Pentagonal Cupola

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

Total Surface Area of Pentagonal Cupola given Height Formula

LaTeX Go

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 Total Surface Area of Pentagonal Cupola given Height?

Total Surface Area of Pentagonal Cupola given Height calculator uses Total Surface Area of Pentagonal Cupola = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(Height of Pentagonal Cupola^(2)/(1-(1/4*cosec(pi/5)^(2)))) to calculate the Total Surface Area of Pentagonal Cupola, The Total Surface Area of Pentagonal Cupola given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Pentagonal Cupola and is calculated using the height of the Pentagonal Cupola. Total Surface Area of Pentagonal Cupola is denoted by TSA symbol.

How to calculate Total Surface Area of Pentagonal Cupola given Height using this online calculator? To use this online calculator for Total Surface Area of Pentagonal Cupola given Height, enter Height of Pentagonal Cupola (h) and hit the calculate button. Here is how the Total Surface Area of Pentagonal Cupola given Height calculation can be explained with given input values -> 1499.652 = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(5^(2)/(1-(1/4*cosec(pi/5)^(2)))).

FAQ

What is Total Surface Area of Pentagonal Cupola given Height?

The Total Surface Area of Pentagonal Cupola given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Pentagonal Cupola and is calculated using the height of the Pentagonal Cupola and is represented as TSA = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(h^(2)/(1-(1/4*cosec(pi/5)^(2)))) or Total Surface Area of Pentagonal Cupola = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(Height of Pentagonal Cupola^(2)/(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 Total Surface Area of Pentagonal Cupola given Height?

The Total Surface Area of Pentagonal Cupola given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Pentagonal Cupola and is calculated using the height of the Pentagonal Cupola is calculated using Total Surface Area of Pentagonal Cupola = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(Height of Pentagonal Cupola^(2)/(1-(1/4*cosec(pi/5)^(2)))). To calculate Total Surface Area 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 Total Surface Area of Pentagonal Cupola?

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

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

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