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Total Surface Area of Rotunda given Height Formula

GoTotal Surface Area of Rotunda Formula

GoTotal Surface Area of Rotunda given Volume Formula

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

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

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

Total Surface Area of Rotunda given Height Example

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

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

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

2312.0716 = \frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))}) \cdot {(\frac{14}{\sqrt{1 + \frac{2}{\sqrt{5}}}})}^{2}

2312.0716m² = \frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))}) \cdot {(\frac{14m}{\sqrt{1 + \frac{2}{\sqrt{5}}}})}^{2}

2312.0716 = \frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))}) \cdot {(\frac{14}{\sqrt{1 + \frac{2}{\sqrt{5}}}})}^{2}

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Total Surface Area of Rotunda given Height Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

TSA = \frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))}) \cdot {(\frac{14m}{\sqrt{1 + \frac{2}{\sqrt{5}}}})}^{2}

Next Step Prepare to Evaluate

∴

TSA = \frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))}) \cdot {(\frac{14}{\sqrt{1 + \frac{2}{\sqrt{5}}}})}^{2}

Next Step Evaluate

∴

TSA = 2312.07157119898m²

LAST Step Rounding Answer

∴

TSA = 2312.0716m²

Total Surface Area of Rotunda given Height Formula Elements

Variables

Functions

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

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

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 Total Surface Area of Rotunda

Go Total Surface Area of Rotunda

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

Go Total Surface Area of Rotunda given Volume

TSA = \frac{1}{2} \cdot ((5 \cdot \sqrt{3}) + \sqrt{10 \cdot (65 + (29 \cdot \sqrt{5}))}) \cdot {(\frac{V}{\frac{1}{12} \cdot (45 + (17 \cdot \sqrt{5}))})}^{\frac{2}{3}}

Go Total Surface Area of Rotunda given Circumsphere Radius

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

Go Total Surface Area of Rotunda given Surface to Volume Ratio

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

How to Evaluate Total Surface Area of Rotunda given Height?

Total Surface Area of Rotunda given Height evaluator uses Total Surface Area of Rotunda = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(Height of Rotunda/(sqrt(1+2/sqrt(5))))^2 to evaluate the Total Surface Area of Rotunda, The Total Surface Area of Rotunda given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Rotunda and is calculated using the height of the Rotunda. Total Surface Area of Rotunda is denoted by TSA symbol.

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

FAQs on Total Surface Area of Rotunda given Height

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

The formula of Total Surface Area of Rotunda given Height is expressed as Total Surface Area of Rotunda = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(Height of Rotunda/(sqrt(1+2/sqrt(5))))^2. Here is an example- 2312.072 = 1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(14/(sqrt(1+2/sqrt(5))))^2.

How to calculate Total Surface Area of Rotunda given Height?

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

What are the other ways to Calculate Total Surface Area of Rotunda?

Here are the different ways to Calculate Total Surface Area of Rotunda-

Total Surface Area of Rotunda=1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*Edge Length of Rotunda^2
Total Surface Area of Rotunda=1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*(Volume of Rotunda/(1/12*(45+(17*sqrt(5)))))^(2/3)
Total Surface Area of Rotunda=1/2*((5*sqrt(3))+sqrt(10*(65+(29*sqrt(5)))))*((2*Circumsphere Radius of Rotunda)/(1+sqrt(5)))^2

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

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

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

Total Surface Area of Rotunda given Height is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Rotunda given Height can be measured.

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