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Surface to Volume Ratio of Frustum of Cone given Volume and Base 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{π \cdot (((r Top + \sqrt{\frac{A Base}{π}}) \cdot \sqrt{{(\frac{3 \cdot V}{π \cdot ({r Top}^{2} + \frac{A Base}{π} + (r Top \cdot \sqrt{\frac{A Base}{π}}))})}^{2} + {(r Top - \sqrt{\frac{A Base}{π}})}^{2}}) + {r Top}^{2} + \frac{A Base}{π})}{V}

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

Surface to Volume Ratio of Frustum of Cone given Volume and Base Area Example

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

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

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

0.5631 = \frac{3.1416 \cdot (((10 + \sqrt{\frac{80}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + \frac{80}{3.1416} + (10 \cdot \sqrt{\frac{80}{3.1416}}))})}^{2} + {(10 - \sqrt{\frac{80}{3.1416}})}^{2}}) + 10^{2} + \frac{80}{3.1416})}{1500}

0.5631m⁻¹ = \frac{3.1416 \cdot (((10m + \sqrt{\frac{80m²}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + \frac{80m²}{3.1416} + (10m \cdot \sqrt{\frac{80m²}{3.1416}}))})}^{2} + {(10m - \sqrt{\frac{80m²}{3.1416}})}^{2}}) + {10m}^{2} + \frac{80m²}{3.1416})}{1500m³}

0.5631 = \frac{3.1416 \cdot (((10 + \sqrt{\frac{80}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + \frac{80}{3.1416} + (10 \cdot \sqrt{\frac{80}{3.1416}}))})}^{2} + {(10 - \sqrt{\frac{80}{3.1416}})}^{2}}) + 10^{2} + \frac{80}{3.1416})}{1500}

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Surface to Volume Ratio of Frustum of Cone given Volume and Base Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

R A/V = \frac{π \cdot (((10m + \sqrt{\frac{80m²}{π}}) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{π \cdot ({10m}^{2} + \frac{80m²}{π} + (10m \cdot \sqrt{\frac{80m²}{π}}))})}^{2} + {(10m - \sqrt{\frac{80m²}{π}})}^{2}}) + {10m}^{2} + \frac{80m²}{π})}{1500m³}

Next Step Substitute values of Constants

∴

R A/V = \frac{3.1416 \cdot (((10m + \sqrt{\frac{80m²}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + \frac{80m²}{3.1416} + (10m \cdot \sqrt{\frac{80m²}{3.1416}}))})}^{2} + {(10m - \sqrt{\frac{80m²}{3.1416}})}^{2}}) + {10m}^{2} + \frac{80m²}{3.1416})}{1500m³}

Next Step Prepare to Evaluate

∴

R A/V = \frac{3.1416 \cdot (((10 + \sqrt{\frac{80}{3.1416}}) \cdot \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + \frac{80}{3.1416} + (10 \cdot \sqrt{\frac{80}{3.1416}}))})}^{2} + {(10 - \sqrt{\frac{80}{3.1416}})}^{2}}) + 10^{2} + \frac{80}{3.1416})}{1500}

Next Step Evaluate

∴

R A/V = 0.563106802837111m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.5631m⁻¹

Surface to Volume Ratio of Frustum of Cone given Volume and Base 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

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 Area of Frustum of Cone

The Base Area of Frustum of Cone is the total amount of two-dimensional space occupied by the base face of the Frustum of the Cone.

Symbol: A_Base

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Base Area of Frustum of Cone

Volume of Frustum of Cone

Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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 Volume and Base Area?

Surface to Volume Ratio of Frustum of Cone given Volume and Base Area evaluator uses Surface to Volume Ratio of Frustum of Cone = (pi*(((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt(((3*Volume of Frustum of Cone)/(pi*(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)))))^2+(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2))+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi))/Volume 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 Volume and Base 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 volume, top radius and base area 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 Volume and Base Area using this online evaluator? To use this online evaluator for Surface to Volume Ratio of Frustum of Cone given Volume and Base Area, enter Top Radius of Frustum of Cone (r_Top), Base Area of Frustum of Cone (A_Base) & Volume of Frustum of Cone (V) and hit the calculate button.

FAQs on Surface to Volume Ratio of Frustum of Cone given Volume and Base Area

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

The formula of Surface to Volume Ratio of Frustum of Cone given Volume and Base Area is expressed as Surface to Volume Ratio of Frustum of Cone = (pi*(((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt(((3*Volume of Frustum of Cone)/(pi*(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)))))^2+(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2))+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi))/Volume of Frustum of Cone. Here is an example- 0.563107 = (pi*(((10+sqrt(80/pi))*sqrt(((3*1500)/(pi*(10^2+80/pi+(10*sqrt(80/pi)))))^2+(10-sqrt(80/pi))^2))+10^2+80/pi))/1500.

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

With Top Radius of Frustum of Cone (r_Top), Base Area of Frustum of Cone (A_Base) & Volume of Frustum of Cone (V) we can find Surface to Volume Ratio of Frustum of Cone given Volume and Base Area using the formula - Surface to Volume Ratio of Frustum of Cone = (pi*(((Top Radius of Frustum of Cone+sqrt(Base Area of Frustum of Cone/pi))*sqrt(((3*Volume of Frustum of Cone)/(pi*(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)))))^2+(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2))+Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi))/Volume 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 Volume and Base Area be negative?

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

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

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

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Surface to Volume Ratio of Frustum of Cone given Volume and Base 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 Volume and Base Area Example

Surface to Volume Ratio of Frustum of Cone given Volume and Base Area Solution

Surface to Volume Ratio of Frustum of Cone given Volume and Base 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 Volume and Base Area?

FAQs on Surface to Volume Ratio of Frustum of Cone given Volume and Base Area

Variable Name

GoSurface to Volume Ratio of Frustum of Cone Formula

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