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Height of Rotunda given Total Surface Area Formula

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GoHeight of Rotunda given Volume Formula

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Height of Rotunda is the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda. Check FAQs

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \sqrt{\frac{TSA}{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}}

h - Height of Rotunda?TSA - Total Surface Area of Rotunda?

Height of Rotunda given Total Surface Area Example

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Here is how the Height of Rotunda given Total Surface Area equation looks like with Values.

Here is how the Height of Rotunda given Total Surface Area equation looks like with Units.

Here is how the Height of Rotunda given Total Surface Area equation looks like.

13.6565 = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \sqrt{\frac{2200}{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}}

13.6565m = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \sqrt{\frac{2200m²}{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}}

13.6565 = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \sqrt{\frac{2200}{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}}

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Height of Rotunda given Total Surface Area Solution

Follow our step by step solution on how to calculate Height of Rotunda given Total Surface Area?

FIRST Step Consider the formula

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \sqrt{\frac{TSA}{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}}

Next Step Substitute values of Variables

∴

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \sqrt{\frac{2200m²}{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}}

Next Step Prepare to Evaluate

∴

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \sqrt{\frac{2200}{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}}

Next Step Evaluate

∴

h = 13.6564789371452m

LAST Step Rounding Answer

∴

h = 13.6565m

Height of Rotunda given Total Surface Area Formula Elements

Variables

Functions

Height of Rotunda

Height of Rotunda is the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Rotunda

Total Surface Area of Rotunda

Total Surface Area of Rotunda is the total amount of two-dimensional space occupied by all the faces of the Rotunda.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Rotunda

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.

Syntax: sqrt(Number)

Other Formulas to find Height of Rotunda

Go Height of Rotunda

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot l e

Go Height of Rotunda given Volume

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot {(\frac{V}{\frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})}^{\frac{1}{3}}

Go Height of Rotunda given Circumsphere Radius

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \frac{2 \cdot r c}{1 + \sqrt{5}}

Go Height of Rotunda given Surface to Volume Ratio

h = \sqrt{1 + \frac{2}{\sqrt{5}}} \cdot \frac{\frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))})}{R A/V \cdot \frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))}

How to Evaluate Height of Rotunda given Total Surface Area?

Height of Rotunda given Total Surface Area evaluator uses Height of Rotunda = sqrt(1+2/sqrt(5))*sqrt(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))) to evaluate the Height of Rotunda, The Height of Rotunda given Total Surface Area formula is defined as the vertical distance from the top pentagonal face to the bottom decagonal face of the Rotunda and is calculated using the total surface area of the Rotunda. Height of Rotunda is denoted by h symbol.

How to evaluate Height of Rotunda given Total Surface Area using this online evaluator? To use this online evaluator for Height of Rotunda given Total Surface Area, enter Total Surface Area of Rotunda (TSA) and hit the calculate button.

FAQs on Height of Rotunda given Total Surface Area

What is the formula to find Height of Rotunda given Total Surface Area?

The formula of Height of Rotunda given Total Surface Area is expressed as Height of Rotunda = sqrt(1+2/sqrt(5))*sqrt(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))). Here is an example- 13.65648 = sqrt(1+2/sqrt(5))*sqrt(2200/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))).

How to calculate Height of Rotunda given Total Surface Area?

With Total Surface Area of Rotunda (TSA) we can find Height of Rotunda given Total Surface Area using the formula - Height of Rotunda = sqrt(1+2/sqrt(5))*sqrt(Total Surface Area of Rotunda/(1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5))))))). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Height of Rotunda?

Here are the different ways to Calculate Height of Rotunda-

Height of Rotunda=sqrt(1+2/sqrt(5))*Edge Length of Rotunda
Height of Rotunda=sqrt(1+2/sqrt(5))*(Volume of Rotunda/(1/12*(45+(17*sqrt(5)))))^(1/3)
Height of Rotunda=sqrt(1+2/sqrt(5))*(2*Circumsphere Radius of Rotunda)/(1+sqrt(5))

Can the Height of Rotunda given Total Surface Area be negative?

No, the Height of Rotunda given Total Surface Area, measured in Length cannot be negative.

Which unit is used to measure Height of Rotunda given Total Surface Area?

Height of Rotunda given Total Surface Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Rotunda given Total Surface Area can be measured.

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