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Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius 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{((\sqrt{{h Slant}^{2} - h^{2}} + 2 \cdot r Base) \cdot h Slant) + {(\sqrt{{h Slant}^{2} - h^{2}} + r Base)}^{2} + {r Base}^{2}}{\frac{1}{3} \cdot h \cdot ({(\sqrt{{h Slant}^{2} - h^{2}} + r Base)}^{2} + {r Base}^{2} + ((\sqrt{{h Slant}^{2} - h^{2}} + r Base) \cdot r Base))}

R_A/V - Surface to Volume Ratio of Frustum of Cone?h_Slant - Slant Height of Frustum of Cone?h - Height of Frustum of Cone?r_Base - Base Radius of Frustum of Cone?

Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius Example

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

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

Here is how the Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius equation looks like.

0.5736 = \frac{((\sqrt{9^{2} - 8^{2}} + 2 \cdot 5) \cdot 9) + {(\sqrt{9^{2} - 8^{2}} + 5)}^{2} + 5^{2}}{\frac{1}{3} \cdot 8 \cdot ({(\sqrt{9^{2} - 8^{2}} + 5)}^{2} + 5^{2} + ((\sqrt{9^{2} - 8^{2}} + 5) \cdot 5))}

0.5736m⁻¹ = \frac{((\sqrt{{9m}^{2} - {8m}^{2}} + 2 \cdot 5m) \cdot 9m) + {(\sqrt{{9m}^{2} - {8m}^{2}} + 5m)}^{2} + {5m}^{2}}{\frac{1}{3} \cdot 8m \cdot ({(\sqrt{{9m}^{2} - {8m}^{2}} + 5m)}^{2} + {5m}^{2} + ((\sqrt{{9m}^{2} - {8m}^{2}} + 5m) \cdot 5m))}

0.5736 = \frac{((\sqrt{9^{2} - 8^{2}} + 2 \cdot 5) \cdot 9) + {(\sqrt{9^{2} - 8^{2}} + 5)}^{2} + 5^{2}}{\frac{1}{3} \cdot 8 \cdot ({(\sqrt{9^{2} - 8^{2}} + 5)}^{2} + 5^{2} + ((\sqrt{9^{2} - 8^{2}} + 5) \cdot 5))}

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3D Geometry » fx Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius

Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius Solution

Follow our step by step solution on how to calculate Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

R A/V = \frac{((\sqrt{{9m}^{2} - {8m}^{2}} + 2 \cdot 5m) \cdot 9m) + {(\sqrt{{9m}^{2} - {8m}^{2}} + 5m)}^{2} + {5m}^{2}}{\frac{1}{3} \cdot 8m \cdot ({(\sqrt{{9m}^{2} - {8m}^{2}} + 5m)}^{2} + {5m}^{2} + ((\sqrt{{9m}^{2} - {8m}^{2}} + 5m) \cdot 5m))}

Next Step Prepare to Evaluate

∴

R A/V = \frac{((\sqrt{9^{2} - 8^{2}} + 2 \cdot 5) \cdot 9) + {(\sqrt{9^{2} - 8^{2}} + 5)}^{2} + 5^{2}}{\frac{1}{3} \cdot 8 \cdot ({(\sqrt{9^{2} - 8^{2}} + 5)}^{2} + 5^{2} + ((\sqrt{9^{2} - 8^{2}} + 5) \cdot 5))}

Next Step Evaluate

∴

R A/V = 0.573637223963953m⁻¹

LAST Step Rounding Answer

∴

R A/V = 0.5736m⁻¹

Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius Formula Elements

Variables

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

Slant Height of Frustum of Cone

The Slant Height of Frustum of Cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases.

Symbol: h_Slant

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Slant Height of Frustum of Cone

Height of Frustum of Cone

Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height 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

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 Slant Height, Height and Base Radius?

Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius evaluator uses Surface to Volume Ratio of Frustum of Cone = (((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+2*Base Radius of Frustum of Cone)*Slant Height of Frustum of Cone)+(sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)^2+Base Radius of Frustum of Cone^2)/(1/3*Height of Frustum of Cone*((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)^2+Base Radius of Frustum of Cone^2+((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base 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 Slant Height, Height and Base Radius 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 slant height, height 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 Slant Height, Height and Base Radius using this online evaluator? To use this online evaluator for Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius, enter Slant Height of Frustum of Cone (h_Slant), Height of Frustum of Cone (h) & Base Radius of Frustum of Cone (r_Base) and hit the calculate button.

FAQs on Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius

What is the formula to find Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius?

The formula of Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius is expressed as Surface to Volume Ratio of Frustum of Cone = (((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+2*Base Radius of Frustum of Cone)*Slant Height of Frustum of Cone)+(sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)^2+Base Radius of Frustum of Cone^2)/(1/3*Height of Frustum of Cone*((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)^2+Base Radius of Frustum of Cone^2+((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)*Base Radius of Frustum of Cone))). Here is an example- 0.573637 = (((sqrt(9^2-8^2)+2*5)*9)+(sqrt(9^2-8^2)+5)^2+5^2)/(1/3*8*((sqrt(9^2-8^2)+5)^2+5^2+((sqrt(9^2-8^2)+5)*5))).

How to calculate Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius?

With Slant Height of Frustum of Cone (h_Slant), Height of Frustum of Cone (h) & Base Radius of Frustum of Cone (r_Base) we can find Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius using the formula - Surface to Volume Ratio of Frustum of Cone = (((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+2*Base Radius of Frustum of Cone)*Slant Height of Frustum of Cone)+(sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)^2+Base Radius of Frustum of Cone^2)/(1/3*Height of Frustum of Cone*((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)^2+Base Radius of Frustum of Cone^2+((sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)+Base Radius of Frustum of Cone)*Base Radius of Frustum of Cone))). This formula also uses 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 Slant Height, Height and Base Radius be negative?

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

Which unit is used to measure Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius?

Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius 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 Slant Height, Height and Base Radius can be measured.

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Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius 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 Slant Height, Height and Base Radius Example

Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius Solution

Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius 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 Slant Height, Height and Base Radius?

FAQs on Surface to Volume Ratio of Frustum of Cone given Slant Height, Height and Base Radius

Variable Name

GoSurface to Volume Ratio of Frustum of Cone Formula

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