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Volume of Pentagonal Cupola given Surface to Volume Ratio Formula

GoVolume of Pentagonal Cupola Formula

GoVolume of Pentagonal Cupola given Height Formula

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

V = \frac{1}{6} \cdot (5 + (4 \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})}^{3}

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

Volume of Pentagonal Cupola given Surface to Volume Ratio Example

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

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

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

2460.0878 = \frac{1}{6} \cdot (5 + (4 \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})}^{3}

2460.0878m³ = \frac{1}{6} \cdot (5 + (4 \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})}^{3}

2460.0878 = \frac{1}{6} \cdot (5 + (4 \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})}^{3}

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Volume of Pentagonal Cupola given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

V = \frac{1}{6} \cdot (5 + (4 \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})}^{3}

Next Step Substitute values of Variables

∴

V = \frac{1}{6} \cdot (5 + (4 \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})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{1}{6} \cdot (5 + (4 \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})}^{3}

Next Step Evaluate

∴

V = 2460.08780847747m³

LAST Step Rounding Answer

∴

V = 2460.0878m³

Volume of Pentagonal Cupola given Surface to Volume Ratio Formula Elements

Variables

Functions

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

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 Volume of Pentagonal Cupola

Go Volume of Pentagonal Cupola

V = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {l e}^{3}

Go Volume of Pentagonal Cupola given Height

V = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{h}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}})}^{3}

Go Volume of Pentagonal Cupola given Total Surface Area

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

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

Volume of Pentagonal Cupola given Surface to Volume Ratio evaluator uses Volume of Pentagonal Cupola = 1/6*(5+(4*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))^3 to evaluate the Volume of Pentagonal Cupola, The Volume of Pentagonal Cupola given Surface to Volume Ratio formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola and is calculated using the surface to volume ratio of the Pentagonal Cupola. Volume of Pentagonal Cupola is denoted by V symbol.

How to evaluate Volume of Pentagonal Cupola given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Volume 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 Volume of Pentagonal Cupola given Surface to Volume Ratio

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

The formula of Volume of Pentagonal Cupola given Surface to Volume Ratio is expressed as Volume of Pentagonal Cupola = 1/6*(5+(4*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))^3. Here is an example- 2460.088 = 1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*0.7))^3.

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

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

What are the other ways to Calculate Volume of Pentagonal Cupola?

Here are the different ways to Calculate Volume of Pentagonal Cupola-

Volume of Pentagonal Cupola=1/6*(5+(4*sqrt(5)))*Edge Length of Pentagonal Cupola^3
Volume of Pentagonal Cupola=1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))^3
Volume of Pentagonal Cupola=1/6*(5+(4*sqrt(5)))*(Total Surface Area of Pentagonal Cupola/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))))^(3/2)

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

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

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

Volume of Pentagonal Cupola given Surface to Volume Ratio is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Pentagonal Cupola given Surface to Volume Ratio can be measured.

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