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Surface to Volume Ratio of Cut Cylindrical Shell Formula

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Surface to Volume Ratio of Cut Cylindrical Shell is the numerical ratio of the total surface area of a Cut Cylindrical Shell to the volume of the Cut Cylindrical Shell. Check FAQs

R A/V = \frac{(π \cdot ((r Outer \cdot (h Short Outer + h Long Outer)) + (r Inner \cdot (h Short Inner + h Long Inner)))) + (π \cdot ({r Outer}^{2} - {r Inner}^{2} + (r Outer \cdot \sqrt{{r Outer}^{2} + {(\frac{h Long Outer - h Short Outer}{2})}^{2}}) - (r Inner \cdot \sqrt{{r Inner}^{2} + {(\frac{h Long Inner - h Short Inner}{2})}^{2}})))}{\frac{π}{2} \cdot (({r Outer}^{2} \cdot (h Short Outer + h Long Outer)) - ({r Inner}^{2} \cdot (h Short Inner + h Long Inner)))}

R_A/V - Surface to Volume Ratio of Cut Cylindrical Shell?r_Outer - Outer Radius of Cut Cylindrical Shell?h_{Short Outer} - Short Outer Height of Cut Cylindrical Shell?h_{Long Outer} - Long Outer Height of Cut Cylindrical Shell?r_Inner - Inner Radius of Cut Cylindrical Shell?h_{Short Inner} - Short Inner Height of Cut Cylindrical Shell?h_{Long Inner} - Long Inner Height of Cut Cylindrical Shell?π - Archimedes' constant?

Surface to Volume Ratio of Cut Cylindrical Shell Example

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Here is how the Surface to Volume Ratio of Cut Cylindrical Shell equation looks like with Values.

Here is how the Surface to Volume Ratio of Cut Cylindrical Shell equation looks like with Units.

Here is how the Surface to Volume Ratio of Cut Cylindrical Shell equation looks like.

0.6121 = \frac{(3.1416 \cdot ((12 \cdot (16 + 20)) + (8 \cdot (17 + 19)))) + (3.1416 \cdot (12^{2} - 8^{2} + (12 \cdot \sqrt{12^{2} + {(\frac{20 - 16}{2})}^{2}}) - (8 \cdot \sqrt{8^{2} + {(\frac{19 - 17}{2})}^{2}})))}{\frac{3.1416}{2} \cdot ((12^{2} \cdot (16 + 20)) - (8^{2} \cdot (17 + 19)))}

0.6121m⁻¹ = \frac{(3.1416 \cdot ((12m \cdot (16m + 20m)) + (8m \cdot (17m + 19m)))) + (3.1416 \cdot ({12m}^{2} - {8m}^{2} + (12m \cdot \sqrt{{12m}^{2} + {(\frac{20m - 16m}{2})}^{2}}) - (8m \cdot \sqrt{{8m}^{2} + {(\frac{19m - 17m}{2})}^{2}})))}{\frac{3.1416}{2} \cdot (({12m}^{2} \cdot (16m + 20m)) - ({8m}^{2} \cdot (17m + 19m)))}

0.6121 = \frac{(3.1416 \cdot ((12 \cdot (16 + 20)) + (8 \cdot (17 + 19)))) + (3.1416 \cdot (12^{2} - 8^{2} + (12 \cdot \sqrt{12^{2} + {(\frac{20 - 16}{2})}^{2}}) - (8 \cdot \sqrt{8^{2} + {(\frac{19 - 17}{2})}^{2}})))}{\frac{3.1416}{2} \cdot ((12^{2} \cdot (16 + 20)) - (8^{2} \cdot (17 + 19)))}

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Surface to Volume Ratio of Cut Cylindrical Shell Solution

Follow our step by step solution on how to calculate Surface to Volume Ratio of Cut Cylindrical Shell?

FIRST Step Consider the formula

R A/V = \frac{(π \cdot ((r Outer \cdot (h Short Outer + h Long Outer)) + (r Inner \cdot (h Short Inner + h Long Inner)))) + (π \cdot ({r Outer}^{2} - {r Inner}^{2} + (r Outer \cdot \sqrt{{r Outer}^{2} + {(\frac{h Long Outer - h Short Outer}{2})}^{2}}) - (r Inner \cdot \sqrt{{r Inner}^{2} + {(\frac{h Long Inner - h Short Inner}{2})}^{2}})))}{\frac{π}{2} \cdot (({r Outer}^{2} \cdot (h Short Outer + h Long Outer)) - ({r Inner}^{2} \cdot (h Short Inner + h Long Inner)))}

Next Step Substitute values of Variables

∴

R A/V = \frac{(π \cdot ((12m \cdot (16m + 20m)) + (8m \cdot (17m + 19m)))) + (π \cdot ({12m}^{2} - {8m}^{2} + (12m \cdot \sqrt{{12m}^{2} + {(\frac{20m - 16m}{2})}^{2}}) - (8m \cdot \sqrt{{8m}^{2} + {(\frac{19m - 17m}{2})}^{2}})))}{\frac{π}{2} \cdot (({12m}^{2} \cdot (16m + 20m)) - ({8m}^{2} \cdot (17m + 19m)))}

Next Step Substitute values of Constants

∴

R A/V = \frac{(3.1416 \cdot ((12m \cdot (16m + 20m)) + (8m \cdot (17m + 19m)))) + (3.1416 \cdot ({12m}^{2} - {8m}^{2} + (12m \cdot \sqrt{{12m}^{2} + {(\frac{20m - 16m}{2})}^{2}}) - (8m \cdot \sqrt{{8m}^{2} + {(\frac{19m - 17m}{2})}^{2}})))}{\frac{3.1416}{2} \cdot (({12m}^{2} \cdot (16m + 20m)) - ({8m}^{2} \cdot (17m + 19m)))}

Next Step Prepare to Evaluate

∴

R A/V = \frac{(3.1416 \cdot ((12 \cdot (16 + 20)) + (8 \cdot (17 + 19)))) + (3.1416 \cdot (12^{2} - 8^{2} + (12 \cdot \sqrt{12^{2} + {(\frac{20 - 16}{2})}^{2}}) - (8 \cdot \sqrt{8^{2} + {(\frac{19 - 17}{2})}^{2}})))}{\frac{3.1416}{2} \cdot ((12^{2} \cdot (16 + 20)) - (8^{2} \cdot (17 + 19)))}

Next Step Evaluate

∴

R A/V = 0.612144610236645m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.6121m⁻¹

Surface to Volume Ratio of Cut Cylindrical Shell Formula Elements

Variables

Constants

Functions

Surface to Volume Ratio of Cut Cylindrical Shell

Surface to Volume Ratio of Cut Cylindrical Shell is the numerical ratio of the total surface area of a Cut Cylindrical Shell to the volume of the Cut Cylindrical Shell.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Cut Cylindrical Shell

Outer Radius of Cut Cylindrical Shell

Outer Radius of Cut Cylindrical Shell is the distance between center and any point on the circumference of the bottom circular face in the outer cut cylinder of the Cut Cylindrical Shell.

Symbol: r_Outer

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Radius of Cut Cylindrical Shell

Short Outer Height of Cut Cylindrical Shell

Short Outer Height of Cut Cylindrical Shell is the shortest vertical distance from the bottom circular face to the top elliptical face of the outer cut cylinder of the Cut Cylindrical Shell.

Symbol: h_{Short Outer}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Outer Height of Cut Cylindrical Shell

Long Outer Height of Cut Cylindrical Shell

Long Outer Height of Cut Cylindrical Shell is the longest vertical distance from the bottom circular face to the top elliptical face of the outer cut cylinder of the Cut Cylindrical Shell.

Symbol: h_{Long Outer}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Outer Height of Cut Cylindrical Shell

Inner Radius of Cut Cylindrical Shell

Inner Radius of Cut Cylindrical Shell is the distance between center and any point on the circumference of the bottom circular face in the inner cut cylinder of the Cut Cylindrical Shell.

Symbol: r_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Radius of Cut Cylindrical Shell

Short Inner Height of Cut Cylindrical Shell

Short Inner Height of Cut Cylindrical Shell is the shortest vertical distance from the bottom circular face to the top elliptical face of the inner cut cylinder of the Cut Cylindrical Shell.

Symbol: h_{Short Inner}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Inner Height of Cut Cylindrical Shell

Long Inner Height of Cut Cylindrical Shell

Long Inner Height of Cut Cylindrical Shell is the longest vertical distance from the bottom circular face to the top elliptical face of the inner cut cylinder of the Cut Cylindrical Shell.

Symbol: h_{Long Inner}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Inner Height of Cut Cylindrical Shell

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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)

How to Evaluate Surface to Volume Ratio of Cut Cylindrical Shell?

Surface to Volume Ratio of Cut Cylindrical Shell evaluator uses Surface to Volume Ratio of Cut Cylindrical Shell = ((pi*((Outer Radius of Cut Cylindrical Shell*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))+(Inner Radius of Cut Cylindrical Shell*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell))))+(pi*(Outer Radius of Cut Cylindrical Shell^2-Inner Radius of Cut Cylindrical Shell^2+(Outer Radius of Cut Cylindrical Shell*sqrt(Outer Radius of Cut Cylindrical Shell^2+((Long Outer Height of Cut Cylindrical Shell-Short Outer Height of Cut Cylindrical Shell)/2)^2))-(Inner Radius of Cut Cylindrical Shell*sqrt(Inner Radius of Cut Cylindrical Shell^2+((Long Inner Height of Cut Cylindrical Shell-Short Inner Height of Cut Cylindrical Shell)/2)^2)))))/(pi/2*((Outer Radius of Cut Cylindrical Shell^2*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))-(Inner Radius of Cut Cylindrical Shell^2*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell)))) to evaluate the Surface to Volume Ratio of Cut Cylindrical Shell, Surface to Volume Ratio of Cut Cylindrical Shell formula is defined as the numerical ratio of the total surface area of a Cut Cylindrical Shell to the volume of the Cut Cylindrical Shell. Surface to Volume Ratio of Cut Cylindrical Shell is denoted by R_A/V symbol.

How to evaluate Surface to Volume Ratio of Cut Cylindrical Shell using this online evaluator? To use this online evaluator for Surface to Volume Ratio of Cut Cylindrical Shell, enter Outer Radius of Cut Cylindrical Shell (r_Outer), Short Outer Height of Cut Cylindrical Shell (h_{Short Outer}), Long Outer Height of Cut Cylindrical Shell (h_{Long Outer}), Inner Radius of Cut Cylindrical Shell (r_Inner), Short Inner Height of Cut Cylindrical Shell (h_{Short Inner}) & Long Inner Height of Cut Cylindrical Shell (h_{Long Inner}) and hit the calculate button.

FAQs on Surface to Volume Ratio of Cut Cylindrical Shell

What is the formula to find Surface to Volume Ratio of Cut Cylindrical Shell?

The formula of Surface to Volume Ratio of Cut Cylindrical Shell is expressed as Surface to Volume Ratio of Cut Cylindrical Shell = ((pi*((Outer Radius of Cut Cylindrical Shell*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))+(Inner Radius of Cut Cylindrical Shell*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell))))+(pi*(Outer Radius of Cut Cylindrical Shell^2-Inner Radius of Cut Cylindrical Shell^2+(Outer Radius of Cut Cylindrical Shell*sqrt(Outer Radius of Cut Cylindrical Shell^2+((Long Outer Height of Cut Cylindrical Shell-Short Outer Height of Cut Cylindrical Shell)/2)^2))-(Inner Radius of Cut Cylindrical Shell*sqrt(Inner Radius of Cut Cylindrical Shell^2+((Long Inner Height of Cut Cylindrical Shell-Short Inner Height of Cut Cylindrical Shell)/2)^2)))))/(pi/2*((Outer Radius of Cut Cylindrical Shell^2*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))-(Inner Radius of Cut Cylindrical Shell^2*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell)))). Here is an example- 0.612145 = ((pi*((12*(16+20))+(8*(17+19))))+(pi*(12^2-8^2+(12*sqrt(12^2+((20-16)/2)^2))-(8*sqrt(8^2+((19-17)/2)^2)))))/(pi/2*((12^2*(16+20))-(8^2*(17+19)))).

How to calculate Surface to Volume Ratio of Cut Cylindrical Shell?

With Outer Radius of Cut Cylindrical Shell (r_Outer), Short Outer Height of Cut Cylindrical Shell (h_{Short Outer}), Long Outer Height of Cut Cylindrical Shell (h_{Long Outer}), Inner Radius of Cut Cylindrical Shell (r_Inner), Short Inner Height of Cut Cylindrical Shell (h_{Short Inner}) & Long Inner Height of Cut Cylindrical Shell (h_{Long Inner}) we can find Surface to Volume Ratio of Cut Cylindrical Shell using the formula - Surface to Volume Ratio of Cut Cylindrical Shell = ((pi*((Outer Radius of Cut Cylindrical Shell*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))+(Inner Radius of Cut Cylindrical Shell*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell))))+(pi*(Outer Radius of Cut Cylindrical Shell^2-Inner Radius of Cut Cylindrical Shell^2+(Outer Radius of Cut Cylindrical Shell*sqrt(Outer Radius of Cut Cylindrical Shell^2+((Long Outer Height of Cut Cylindrical Shell-Short Outer Height of Cut Cylindrical Shell)/2)^2))-(Inner Radius of Cut Cylindrical Shell*sqrt(Inner Radius of Cut Cylindrical Shell^2+((Long Inner Height of Cut Cylindrical Shell-Short Inner Height of Cut Cylindrical Shell)/2)^2)))))/(pi/2*((Outer Radius of Cut Cylindrical Shell^2*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))-(Inner Radius of Cut Cylindrical Shell^2*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell)))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Surface to Volume Ratio of Cut Cylindrical Shell be negative?

No, the Surface to Volume Ratio of Cut Cylindrical Shell, measured in Reciprocal Length cannot be negative.

Which unit is used to measure Surface to Volume Ratio of Cut Cylindrical Shell?

Surface to Volume Ratio of Cut Cylindrical Shell is usually measured using the 1 per Meter[m⁻¹] for Reciprocal Length. 1 per Kilometer[m⁻¹], 1 per Mile[m⁻¹], 1 per Yard[m⁻¹] are the few other units in which Surface to Volume Ratio of Cut Cylindrical Shell can be measured.

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Surface to Volume Ratio of Cut Cylindrical Shell Formula

Surface to Volume Ratio of Cut Cylindrical Shell Example

Surface to Volume Ratio of Cut Cylindrical Shell Solution

Surface to Volume Ratio of Cut Cylindrical Shell Formula Elements

How to Evaluate Surface to Volume Ratio of Cut Cylindrical Shell?

FAQs on Surface to Volume Ratio of Cut Cylindrical Shell

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