Height of Triangular Cupola given Total Surface Area Calculator

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

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✖Height of Triangular Cupola is the vertical distance from the triangular face to the opposite hexagonal face of the Triangular Cupola.ⓘ Height of Triangular Cupola given Total Surface Area [h]

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Height of Triangular Cupola given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Height of Triangular Cupola - (Measured in Meter) - Height of Triangular Cupola is the vertical distance from the triangular face to the opposite hexagonal face of the Triangular Cupola.
Total Surface Area of Triangular Cupola - (Measured in Square Meter) - Total Surface Area of Triangular Cupola is the total amount of 2D space occupied by all the faces of the Triangular Cupola.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Triangular Cupola: 730 Square Meter --> 730 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = sqrt(TSA/(3+(5*sqrt(3))/2))*sqrt(1-(1/4*cosec(pi/3)^(2))) --> sqrt(730/(3+(5*sqrt(3))/2))*sqrt(1-(1/4*cosec(pi/3)^(2)))

Evaluating ... ...

h = 8.14816941871708

STEP 3: Convert Result to Output's Unit

8.14816941871708 Meter --> No Conversion Required

FINAL ANSWER

8.14816941871708 ≈ 8.148169 Meter <-- Height of Triangular Cupola

(Calculation completed in 00.007 seconds)

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St Joseph's College (SJC), Bengaluru

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< Height of Triangular Cupola Calculators

Height of Triangular Cupola given Surface to Volume Ratio

LaTeX Go Height of Triangular Cupola = ((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola)*sqrt(1-(1/4*cosec(pi/3)^(2)))

Height of Triangular Cupola given Total Surface Area

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

Height of Triangular Cupola given Volume

LaTeX Go Height of Triangular Cupola = ((3*sqrt(2)*Volume of Triangular Cupola)/5)^(1/3)*sqrt(1-(1/4*cosec(pi/3)^(2)))

Height of Triangular Cupola

LaTeX Go Height of Triangular Cupola = Edge Length of Triangular Cupola*sqrt(1-(1/4*cosec(pi/3)^(2)))

Height of Triangular Cupola given Total Surface Area Formula

LaTeX Go

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

What is a Triangular 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 Triangular Cupola has 8 faces, 15 edges, and 9 vertices. Its top surface is an equilateral triangle and its base surface is a regular hexagon.

How to Calculate Height of Triangular Cupola given Total Surface Area?

Height of Triangular Cupola given Total Surface Area calculator uses Height of Triangular Cupola = sqrt(Total Surface Area of Triangular Cupola/(3+(5*sqrt(3))/2))*sqrt(1-(1/4*cosec(pi/3)^(2))) to calculate the Height of Triangular Cupola, The Height of Triangular Cupola given Total Surface Area formula is defined as the vertical distance from the triangular face to the opposite hexagonal face of the Triangular Cupola and is calculated using the total surface area of the Triangular Cupola. Height of Triangular Cupola is denoted by h symbol.

How to calculate Height of Triangular Cupola given Total Surface Area using this online calculator? To use this online calculator for Height of Triangular Cupola given Total Surface Area, enter Total Surface Area of Triangular Cupola (TSA) and hit the calculate button. Here is how the Height of Triangular Cupola given Total Surface Area calculation can be explained with given input values -> 8.148169 = sqrt(730/(3+(5*sqrt(3))/2))*sqrt(1-(1/4*cosec(pi/3)^(2))).

FAQ

What is Height of Triangular Cupola given Total Surface Area?

The Height of Triangular Cupola given Total Surface Area formula is defined as the vertical distance from the triangular face to the opposite hexagonal face of the Triangular Cupola and is calculated using the total surface area of the Triangular Cupola and is represented as h = sqrt(TSA/(3+(5*sqrt(3))/2))*sqrt(1-(1/4*cosec(pi/3)^(2))) or Height of Triangular Cupola = sqrt(Total Surface Area of Triangular Cupola/(3+(5*sqrt(3))/2))*sqrt(1-(1/4*cosec(pi/3)^(2))). Total Surface Area of Triangular Cupola is the total amount of 2D space occupied by all the faces of the Triangular Cupola.

How to calculate Height of Triangular Cupola given Total Surface Area?

The Height of Triangular Cupola given Total Surface Area formula is defined as the vertical distance from the triangular face to the opposite hexagonal face of the Triangular Cupola and is calculated using the total surface area of the Triangular Cupola is calculated using Height of Triangular Cupola = sqrt(Total Surface Area of Triangular Cupola/(3+(5*sqrt(3))/2))*sqrt(1-(1/4*cosec(pi/3)^(2))). To calculate Height of Triangular Cupola given Total Surface Area, you need Total Surface Area of Triangular Cupola (TSA). With our tool, you need to enter the respective value for Total Surface Area of Triangular 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 Height of Triangular Cupola?

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

Height of Triangular Cupola = Edge Length of Triangular Cupola*sqrt(1-(1/4*cosec(pi/3)^(2)))
Height of Triangular Cupola = ((3*sqrt(2)*Volume of Triangular Cupola)/5)^(1/3)*sqrt(1-(1/4*cosec(pi/3)^(2)))
Height of Triangular Cupola = ((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola)*sqrt(1-(1/4*cosec(pi/3)^(2)))

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