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Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio 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{\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}

TSA - Total Surface Area of Pentagonal Cupola?R_A/V - Surface to Volume Ratio of Pentagonal Cupola?

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

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

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

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

1722.0615 = \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 0.7})}^{2}

1722.0615m² = \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 0.7m⁻¹})}^{2}

1722.0615 = \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 0.7})}^{2}

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

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

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{\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}

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{\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 0.7m⁻¹})}^{2}

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{\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 0.7})}^{2}

Next Step Evaluate

∴

TSA = 1722.06146593423m²

LAST Step Rounding Answer

∴

TSA = 1722.0615m²

Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio Formula Elements

Variables

Functions

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

Surface to Volume Ratio of Pentagonal Cupola

Surface to Volume Ratio of Pentagonal Cupola is the numerical ratio of the total surface area of a Pentagonal Cupola to the volume of the Pentagonal Cupola.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio 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 Volume

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}}

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

Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio evaluator uses 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 to evaluate the Total Surface Area of Pentagonal Cupola, The Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio 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 surface to volume ratio 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 Surface to Volume Ratio using this online evaluator? To use this online evaluator for Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio, enter Surface to Volume Ratio of Pentagonal Cupola (R_A/V) and hit the calculate button.

FAQs on Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio

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

The formula of Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio is expressed as 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. Here is an example- 1722.061 = 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)))*0.7))^2.

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

With Surface to Volume Ratio of Pentagonal Cupola (R_A/V) we can find Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio using the formula - 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. This formula also uses Square Root (sqrt) 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)))))*(Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(2/3)

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

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

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

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

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