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Surface to Volume Ratio of Frustum of Cone given Total Surface Area Formula

GoSurface to Volume Ratio of Frustum of Cone Formula

GoSurface to Volume Ratio of Frustum of Cone given Base Area Formula

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Surface to Volume Ratio of Frustum of Cone is the numerical ratio of the total surface area of a Frustum of Cone to the volume of the Frustum of Cone. Check FAQs

R A/V = \frac{TSA}{\frac{1}{3} \cdot π \cdot \sqrt{{(\frac{\frac{TSA}{π} - ({r Top}^{2} + {r Base}^{2})}{r Top + r Base})}^{2} - {(r Top - r Base)}^{2}} \cdot ({r Top}^{2} + {r Base}^{2} + (r Top \cdot r Base))}

R_A/V - Surface to Volume Ratio of Frustum of Cone?TSA - Total Surface Area of Frustum of Cone?r_Top - Top Radius of Frustum of Cone?r_Base - Base Radius of Frustum of Cone?π - Archimedes' constant?

Surface to Volume Ratio of Frustum of Cone given Total Surface Area Example

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

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

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

0.5577 = \frac{850}{\frac{1}{3} \cdot 3.1416 \cdot \sqrt{{(\frac{\frac{850}{3.1416} - (10^{2} + 5^{2})}{10 + 5})}^{2} - {(10 - 5)}^{2}} \cdot (10^{2} + 5^{2} + (10 \cdot 5))}

0.5577m⁻¹ = \frac{850m²}{\frac{1}{3} \cdot 3.1416 \cdot \sqrt{{(\frac{\frac{850m²}{3.1416} - ({10m}^{2} + {5m}^{2})}{10m + 5m})}^{2} - {(10m - 5m)}^{2}} \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))}

0.5577 = \frac{850}{\frac{1}{3} \cdot 3.1416 \cdot \sqrt{{(\frac{\frac{850}{3.1416} - (10^{2} + 5^{2})}{10 + 5})}^{2} - {(10 - 5)}^{2}} \cdot (10^{2} + 5^{2} + (10 \cdot 5))}

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Surface to Volume Ratio of Frustum of Cone given Total Surface Area Solution

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

FIRST Step Consider the formula

R A/V = \frac{TSA}{\frac{1}{3} \cdot π \cdot \sqrt{{(\frac{\frac{TSA}{π} - ({r Top}^{2} + {r Base}^{2})}{r Top + r Base})}^{2} - {(r Top - r Base)}^{2}} \cdot ({r Top}^{2} + {r Base}^{2} + (r Top \cdot r Base))}

Next Step Substitute values of Variables

∴

R A/V = \frac{850m²}{\frac{1}{3} \cdot π \cdot \sqrt{{(\frac{\frac{850m²}{π} - ({10m}^{2} + {5m}^{2})}{10m + 5m})}^{2} - {(10m - 5m)}^{2}} \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))}

Next Step Substitute values of Constants

∴

R A/V = \frac{850m²}{\frac{1}{3} \cdot 3.1416 \cdot \sqrt{{(\frac{\frac{850m²}{3.1416} - ({10m}^{2} + {5m}^{2})}{10m + 5m})}^{2} - {(10m - 5m)}^{2}} \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))}

Next Step Prepare to Evaluate

∴

R A/V = \frac{850}{\frac{1}{3} \cdot 3.1416 \cdot \sqrt{{(\frac{\frac{850}{3.1416} - (10^{2} + 5^{2})}{10 + 5})}^{2} - {(10 - 5)}^{2}} \cdot (10^{2} + 5^{2} + (10 \cdot 5))}

Next Step Evaluate

∴

R A/V = 0.557682519403272m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.5577m⁻¹

Surface to Volume Ratio of Frustum of Cone given Total Surface Area Formula Elements

Variables

Constants

Functions

Surface to Volume Ratio of Frustum of Cone

Surface to Volume Ratio of Frustum of Cone is the numerical ratio of the total surface area of a Frustum of Cone to the volume of the Frustum of Cone.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio of Frustum of Cone

Total Surface Area of Frustum of Cone

Total Surface Area of Frustum of Cone is the total quantity of plane enclosed on the entire surface of the Frustum of the Cone.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Frustum of Cone

Top Radius of Frustum of Cone

Top Radius of Frustum of Cone is the distance between the center and any point on the circumference of the top circular surface of the Frustum of the Cone.

Symbol: r_Top

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Top Radius of Frustum of Cone

Base Radius of Frustum of Cone

Base Radius of Frustum of Cone is the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone.

Symbol: r_Base

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Base Radius of Frustum of Cone

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)

Other Formulas to find Surface to Volume Ratio of Frustum of Cone

Go Surface to Volume Ratio of Frustum of Cone

R A/V = \frac{((r Top + r Base) \cdot \sqrt{{(r Top - r Base)}^{2} + h^{2}}) + {r Top}^{2} + {r Base}^{2}}{\frac{1}{3} \cdot h \cdot ({r Top}^{2} + {r Base}^{2} + (r Top \cdot r Base))}

Go Surface to Volume Ratio of Frustum of Cone given Base Area

R A/V = \frac{((r Top + \sqrt{\frac{A Base}{π}}) \cdot \sqrt{{(r Top - \sqrt{\frac{A Base}{π}})}^{2} + h^{2}}) + {r Top}^{2} + A Base}{\frac{1}{3} \cdot h \cdot ({r Top}^{2} + \frac{A Base}{π} + (r Top \cdot \sqrt{\frac{A Base}{π}}))}

Go Surface to Volume Ratio of Frustum of Cone given Base Area and Top Area

R A/V = \frac{((\sqrt{\frac{A Top}{π}} + \sqrt{\frac{A Base}{π}}) \cdot \sqrt{{(\sqrt{\frac{A Top}{π}} - \sqrt{\frac{A Base}{π}})}^{2} + h^{2}}) + \frac{A Top}{π} + \frac{A Base}{π}}{\frac{1}{3} \cdot h \cdot (\frac{A Top}{π} + \frac{A Base}{π} + (\sqrt{\frac{A Top}{π}} \cdot \sqrt{\frac{A Base}{π}}))}

Go Surface to Volume Ratio of Frustum of Cone given Slant Height

R A/V = \frac{((r Top + r Base) \cdot h Slant) + {r Top}^{2} + {r Base}^{2}}{\frac{\sqrt{{h Slant}^{2} - {(r Top - r Base)}^{2}}}{3} \cdot ({r Top}^{2} + {r Base}^{2} + (r Top \cdot r Base))}

How to Evaluate Surface to Volume Ratio of Frustum of Cone given Total Surface Area?

Surface to Volume Ratio of Frustum of Cone given Total Surface Area evaluator uses Surface to Volume Ratio of Frustum of Cone = Total Surface Area of Frustum of Cone/(1/3*pi*sqrt(((Total Surface Area of Frustum of Cone/pi-(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2))/(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone))^2-(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))) to evaluate the Surface to Volume Ratio of Frustum of Cone, The Surface to Volume Ratio of Frustum of Cone given Total Surface Area formula is defined as the numerical ratio of the total surface area of a Frustum of Cone to the volume of the Frustum of Cone, calculated using the total surface area, top radius and base radius of the Frustum of Cone. Surface to Volume Ratio of Frustum of Cone is denoted by R_A/V symbol.

How to evaluate Surface to Volume Ratio of Frustum of Cone given Total Surface Area using this online evaluator? To use this online evaluator for Surface to Volume Ratio of Frustum of Cone given Total Surface Area, enter Total Surface Area of Frustum of Cone (TSA), Top Radius of Frustum of Cone (r_Top) & Base Radius of Frustum of Cone (r_Base) and hit the calculate button.

FAQs on Surface to Volume Ratio of Frustum of Cone given Total Surface Area

What is the formula to find Surface to Volume Ratio of Frustum of Cone given Total Surface Area?

The formula of Surface to Volume Ratio of Frustum of Cone given Total Surface Area is expressed as Surface to Volume Ratio of Frustum of Cone = Total Surface Area of Frustum of Cone/(1/3*pi*sqrt(((Total Surface Area of Frustum of Cone/pi-(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2))/(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone))^2-(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))). Here is an example- 0.557683 = 850/(1/3*pi*sqrt(((850/pi-(10^2+5^2))/(10+5))^2-(10-5)^2)*(10^2+5^2+(10*5))).

How to calculate Surface to Volume Ratio of Frustum of Cone given Total Surface Area?

With Total Surface Area of Frustum of Cone (TSA), Top Radius of Frustum of Cone (r_Top) & Base Radius of Frustum of Cone (r_Base) we can find Surface to Volume Ratio of Frustum of Cone given Total Surface Area using the formula - Surface to Volume Ratio of Frustum of Cone = Total Surface Area of Frustum of Cone/(1/3*pi*sqrt(((Total Surface Area of Frustum of Cone/pi-(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2))/(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone))^2-(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Surface to Volume Ratio of Frustum of Cone?

Here are the different ways to Calculate Surface to Volume Ratio of Frustum of Cone-

Surface to Volume Ratio of Frustum of Cone=(((Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)*sqrt((Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2+Height of Frustum of Cone^2))+Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2)/(1/3*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone)))
Surface to Volume Ratio of Frustum of Cone=(((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt((Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2+Height of Frustum of Cone^2))+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone)/(1/3*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi+(Top Radius of Frustum of Cone*sqrt(Base Area of Frustum of Cone/pi))))
Surface to Volume Ratio of Frustum of Cone=(((sqrt(Top Area of Frustum of Cone/pi)+sqrt(Base Area of Frustum of Cone/pi))*sqrt((sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2+Height of Frustum of Cone^2))+Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi)/(1/3*Height of Frustum of Cone*(Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi+(sqrt(Top Area of Frustum of Cone/pi)*sqrt(Base Area of Frustum of Cone/pi))))

Can the Surface to Volume Ratio of Frustum of Cone given Total Surface Area be negative?

No, the Surface to Volume Ratio of Frustum of Cone given Total Surface Area, measured in Reciprocal Length cannot be negative.

Which unit is used to measure Surface to Volume Ratio of Frustum of Cone given Total Surface Area?

Surface to Volume Ratio of Frustum of Cone given Total Surface Area 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 Frustum of Cone given Total Surface Area can be measured.

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Surface to Volume Ratio of Frustum of Cone given Total Surface Area Formula

​GoSurface to Volume Ratio of Frustum of Cone Formula

​GoSurface to Volume Ratio of Frustum of Cone given Base Area Formula

Surface to Volume Ratio of Frustum of Cone given Total Surface Area Example

Surface to Volume Ratio of Frustum of Cone given Total Surface Area Solution

Surface to Volume Ratio of Frustum of Cone given Total Surface Area Formula Elements

Other Formulas to find Surface to Volume Ratio of Frustum of Cone

How to Evaluate Surface to Volume Ratio of Frustum of Cone given Total Surface Area?

FAQs on Surface to Volume Ratio of Frustum of Cone given Total Surface Area

Variable Name

GoSurface to Volume Ratio of Frustum of Cone Formula

GoSurface to Volume Ratio of Frustum of Cone given Base Area Formula