Total Surface Area of Pentagonal Cupola given Volume 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)))))*(Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(2/3)
TSA = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(V/(1/6*(5+(4*sqrt(5)))))^(2/3)
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.
Volume of Pentagonal Cupola - (Measured in Cubic Meter) - Volume of Pentagonal Cupola is the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola.
STEP 1: Convert Input(s) to Base Unit
Volume of Pentagonal Cupola: 2300 Cubic Meter --> 2300 Cubic 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)))))*(V/(1/6*(5+(4*sqrt(5)))))^(2/3) --> 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(2300/(1/6*(5+(4*sqrt(5)))))^(2/3)
Evaluating ... ...
TSA = 1646.51920343986
STEP 3: Convert Result to Output's Unit
1646.51920343986 Square Meter --> No Conversion Required
FINAL ANSWER
1646.51920343986 1646.519 Square Meter <-- Total Surface Area of Pentagonal Cupola
(Calculation completed in 00.004 seconds)

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4 Total Surface Area of Pentagonal Cupola Calculators

Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio
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
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
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
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 Volume Formula

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)
TSA = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(V/(1/6*(5+(4*sqrt(5)))))^(2/3)

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 Volume?

Total Surface Area of Pentagonal Cupola given Volume calculator uses 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) to calculate the Total Surface Area of Pentagonal Cupola, The Total Surface Area of Pentagonal Cupola given Volume 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 volume 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 Volume using this online calculator? To use this online calculator for Total Surface Area of Pentagonal Cupola given Volume, enter Volume of Pentagonal Cupola (V) and hit the calculate button. Here is how the Total Surface Area of Pentagonal Cupola given Volume calculation can be explained with given input values -> 1646.519 = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(2300/(1/6*(5+(4*sqrt(5)))))^(2/3).

FAQ

What is Total Surface Area of Pentagonal Cupola given Volume?
The Total Surface Area of Pentagonal Cupola given Volume 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 volume of the Pentagonal Cupola and is represented as TSA = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(V/(1/6*(5+(4*sqrt(5)))))^(2/3) or 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). Volume of Pentagonal Cupola is the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola.
How to calculate Total Surface Area of Pentagonal Cupola given Volume?
The Total Surface Area of Pentagonal Cupola given Volume 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 volume 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)))))*(Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(2/3). To calculate Total Surface Area of Pentagonal Cupola given Volume, you need Volume of Pentagonal Cupola (V). With our tool, you need to enter the respective value for Volume 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 Volume 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)))))*((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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