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Total Surface Area of Pentagonal Cupola given Volume Formula

GoTotal Surface Area of Pentagonal Cupola Formula

GoTotal Surface Area of Pentagonal Cupola given Height Formula

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Total Surface Area of Pentagonal Cupola is the total amount of 2D space occupied by all the faces of the Pentagonal Cupola. Check FAQs

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {(\frac{V}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{2}{3}}

TSA - Total Surface Area of Pentagonal Cupola?V - Volume of Pentagonal Cupola?

Total Surface Area of Pentagonal Cupola given Volume Example

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Here is how the Total Surface Area of Pentagonal Cupola given Volume equation looks like with Values.

Here is how the Total Surface Area of Pentagonal Cupola given Volume equation looks like with Units.

Here is how the Total Surface Area of Pentagonal Cupola given Volume equation looks like.

1646.5192 = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {(\frac{2300}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{2}{3}}

1646.5192m² = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {(\frac{2300m³}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{2}{3}}

1646.5192 = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {(\frac{2300}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{2}{3}}

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Total Surface Area of Pentagonal Cupola given Volume Solution

Follow our step by step solution on how to calculate Total Surface Area of Pentagonal Cupola given Volume?

FIRST Step Consider the formula

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {(\frac{V}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{2}{3}}

Next Step Substitute values of Variables

∴

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {(\frac{2300m³}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{2}{3}}

Next Step Prepare to Evaluate

∴

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {(\frac{2300}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{2}{3}}

Next Step Evaluate

∴

TSA = 1646.51920343986m²

LAST Step Rounding Answer

∴

TSA = 1646.5192m²

Total Surface Area of Pentagonal Cupola given Volume Formula Elements

Variables

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Total Surface Area of Pentagonal Cupola

Total Surface Area of Pentagonal Cupola is the total amount of 2D space occupied by all the faces of the Pentagonal Cupola.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Pentagonal Cupola

Volume of Pentagonal Cupola

Volume of Pentagonal Cupola is the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Pentagonal Cupola

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 Pentagonal Cupola

Go Total Surface Area of Pentagonal Cupola

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {l e}^{2}

Go Total Surface Area of Pentagonal Cupola given Height

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot (\frac{h^{2}}{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})})

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

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {(\frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot R A/V})}^{2}

How to Evaluate Total Surface Area of Pentagonal Cupola given Volume?

Total Surface Area of Pentagonal Cupola given Volume evaluator 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 evaluate 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 evaluate Total Surface Area of Pentagonal Cupola given Volume using this online evaluator? To use this online evaluator for Total Surface Area of Pentagonal Cupola given Volume, enter Volume of Pentagonal Cupola (V) and hit the calculate button.

FAQs on Total Surface Area of Pentagonal Cupola given Volume

What is the formula to find Total Surface Area of Pentagonal Cupola given Volume?

The formula of Total Surface Area of Pentagonal Cupola given Volume is expressed as 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). Here is an example- 1646.519 = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(2300/(1/6*(5+(4*sqrt(5)))))^(2/3).

How to calculate Total Surface Area of Pentagonal Cupola given Volume?

With Volume of Pentagonal Cupola (V) we can find Total Surface Area of Pentagonal Cupola given Volume using the 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). This formula also uses Square Root Function function(s).

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

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

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

Can the Total Surface Area of Pentagonal Cupola given Volume be negative?

No, the Total Surface Area of Pentagonal Cupola given Volume, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Pentagonal Cupola given Volume?

Total Surface Area of Pentagonal Cupola given Volume 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 Pentagonal Cupola given Volume can be measured.

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