Total Surface Area 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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✖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 Surface to Volume Ratio [TSA]

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Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio 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)))))*((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
TSA = 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)))*R_A/V))^2
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

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.
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

TSA = 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)))*R_A/V))^2 --> 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)))*0.7))^2

Evaluating ... ...

TSA = 1722.06146593423

STEP 3: Convert Result to Output's Unit

1722.06146593423 Square Meter --> No Conversion Required

FINAL ANSWER

1722.06146593423 ≈ 1722.061 Square Meter <-- Total Surface Area of Pentagonal Cupola

(Calculation completed in 00.020 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 Surface to Volume Ratio 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 Surface to Volume Ratio?

Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio calculator uses 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 to calculate the Total Surface Area of Pentagonal Cupola, The Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio 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 surface to volume ratio 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 Surface to Volume Ratio using this online calculator? To use this online calculator for Total Surface Area 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 Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio calculation can be explained with given input values -> 1722.061 = 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)))*0.7))^2.

FAQ

What is Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio?

The Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio 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 surface to volume ratio of the Pentagonal Cupola and is represented as TSA = 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)))*R_A/V))^2 or 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. 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 Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio?

The Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio 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 surface to volume ratio 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)))))*((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. To calculate Total Surface Area 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 Total Surface Area of Pentagonal Cupola?

In this formula, Total Surface Area 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 -

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

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