Edge Length of Square Cupola given Total Surface Area Calculator

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

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✖Edge Length of Square Cupola is the length of any edge of the Square Cupola.ⓘ Edge Length of Square Cupola given Total Surface Area [l_e]

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Formula

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Edge Length of Square Cupola given Total Surface Area

Formula

`"l"_{"e"} = sqrt("TSA"/(7+(2*sqrt(2))+sqrt(3)))`

Example

`"10.01708m"=sqrt("1160m²"/(7+(2*sqrt(2))+sqrt(3)))`

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Edge Length of Square Cupola given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Square Cupola = sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3)))
l_e = sqrt(TSA/(7+(2*sqrt(2))+sqrt(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

Edge Length of Square Cupola - (Measured in Meter) - Edge Length of Square Cupola is the length of any edge of the Square Cupola.
Total Surface Area of Square Cupola - (Measured in Square Meter) - Total Surface Area of Square Cupola is the total amount of 2D space occupied by all the faces of the Square Cupola.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Square Cupola: 1160 Square Meter --> 1160 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = sqrt(TSA/(7+(2*sqrt(2))+sqrt(3))) --> sqrt(1160/(7+(2*sqrt(2))+sqrt(3)))

Evaluating ... ...

l_e = 10.0170790285602

STEP 3: Convert Result to Output's Unit

10.0170790285602 Meter --> No Conversion Required

FINAL ANSWER

10.0170790285602 ≈ 10.01708 Meter <-- Edge Length of Square Cupola

(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru

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< 4 Edge Length of Square Cupola Calculators

Edge Length of Square Cupola given Surface to Volume Ratio

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

Edge Length of Square Cupola given Total Surface Area

Go Edge Length of Square Cupola = sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3)))

Edge Length of Square Cupola given Height

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

Edge Length of Square Cupola given Volume

Go Edge Length of Square Cupola = (Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3)

Edge Length of Square Cupola given Total Surface Area Formula

Edge Length of Square Cupola = sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3)))
l_e = sqrt(TSA/(7+(2*sqrt(2))+sqrt(3)))

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 Edge Length of Square Cupola given Total Surface Area?

Edge Length of Square Cupola given Total Surface Area calculator uses Edge Length of Square Cupola = sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3))) to calculate the Edge Length of Square Cupola, The Edge Length of Square Cupola given Total Surface Area formula is defined as the length of any edge of the Square Cupola and is calculated using the total surface area of the Square Cupola. Edge Length of Square Cupola is denoted by l_e symbol.

How to calculate Edge Length of Square Cupola given Total Surface Area using this online calculator? To use this online calculator for Edge Length of Square Cupola given Total Surface Area, enter Total Surface Area of Square Cupola (TSA) and hit the calculate button. Here is how the Edge Length of Square Cupola given Total Surface Area calculation can be explained with given input values -> 10.01708 = sqrt(1160/(7+(2*sqrt(2))+sqrt(3))).

FAQ

What is Edge Length of Square Cupola given Total Surface Area?

The Edge Length of Square Cupola given Total Surface Area formula is defined as the length of any edge of the Square Cupola and is calculated using the total surface area of the Square Cupola and is represented as l_e = sqrt(TSA/(7+(2*sqrt(2))+sqrt(3))) or Edge Length of Square Cupola = sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3))). Total Surface Area of Square Cupola is the total amount of 2D space occupied by all the faces of the Square Cupola.

How to calculate Edge Length of Square Cupola given Total Surface Area?

The Edge Length of Square Cupola given Total Surface Area formula is defined as the length of any edge of the Square Cupola and is calculated using the total surface area of the Square Cupola is calculated using Edge Length of Square Cupola = sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3))). To calculate Edge Length of Square Cupola given Total Surface Area, you need Total Surface Area of Square Cupola (TSA). With our tool, you need to enter the respective value for Total Surface Area 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 Edge Length of Square Cupola?

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

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

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