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Slant Height of Frustum of Cone given Volume Formula

GoSlant Height of Frustum of Cone Formula

GoSlant Height of Frustum of Cone given Curved Surface Area Formula

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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. Check FAQs

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

h_Slant - Slant Height of Frustum of Cone?V - Volume of Frustum of Cone?r_Top - Top Radius of Frustum of Cone?r_Base - Base Radius of Frustum of Cone?π - Archimedes' constant?

Slant Height of Frustum of Cone given Volume Example

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Here is how the Slant Height of Frustum of Cone given Volume equation looks like with Values.

Here is how the Slant Height of Frustum of Cone given Volume equation looks like with Units.

Here is how the Slant Height of Frustum of Cone given Volume equation looks like.

9.5915 = \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))})}^{2} + {(10 - 5)}^{2}}

9.5915m = \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))})}^{2} + {(10m - 5m)}^{2}}

9.5915 = \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))})}^{2} + {(10 - 5)}^{2}}

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Slant Height of Frustum of Cone given Volume Solution

Follow our step by step solution on how to calculate Slant Height of Frustum of Cone given Volume?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h Slant = \sqrt{{(\frac{3 \cdot 1500m³}{π \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))})}^{2} + {(10m - 5m)}^{2}}

Next Step Substitute values of Constants

∴

h Slant = \sqrt{{(\frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))})}^{2} + {(10m - 5m)}^{2}}

Next Step Prepare to Evaluate

∴

h Slant = \sqrt{{(\frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))})}^{2} + {(10 - 5)}^{2}}

Next Step Evaluate

∴

h Slant = 9.59145703005666m

LAST Step Rounding Answer

∴

h Slant = 9.5915m

Slant Height of Frustum of Cone given Volume Formula Elements

Variables

Constants

Functions

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

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

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 Slant Height of Frustum of Cone

Go Slant Height of Frustum of Cone

h Slant = \sqrt{h^{2} + {(r Top - r Base)}^{2}}

Go Slant Height of Frustum of Cone given Curved Surface Area

h Slant = \frac{CSA}{π \cdot (r Top + r Base)}

Go Slant Height of Frustum of Cone given Total Surface Area

h Slant = \frac{\frac{TSA}{π} - ({r Top}^{2} + {r Base}^{2})}{r Top + r Base}

How to Evaluate Slant Height of Frustum of Cone given Volume?

Slant Height of Frustum of Cone given Volume evaluator uses Slant Height of Frustum of Cone = sqrt(((3*Volume 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) to evaluate the Slant Height of Frustum of Cone, The Slant Height of Frustum of Cone given Volume formula is defined as the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases of Frustum of Cone, calculated using volume of Frustum of Cone. Slant Height of Frustum of Cone is denoted by h_Slant symbol.

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

FAQs on Slant Height of Frustum of Cone given Volume

What is the formula to find Slant Height of Frustum of Cone given Volume?

The formula of Slant Height of Frustum of Cone given Volume is expressed as Slant Height of Frustum of Cone = sqrt(((3*Volume 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). Here is an example- 9.591457 = sqrt(((3*1500)/(pi*(10^2+5^2+(10*5))))^2+(10-5)^2).

How to calculate Slant Height of Frustum of Cone given Volume?

With Volume of Frustum of Cone (V), Top Radius of Frustum of Cone (r_Top) & Base Radius of Frustum of Cone (r_Base) we can find Slant Height of Frustum of Cone given Volume using the formula - Slant Height of Frustum of Cone = sqrt(((3*Volume 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). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Slant Height of Frustum of Cone?

Here are the different ways to Calculate Slant Height of Frustum of Cone-

Slant Height of Frustum of Cone=sqrt(Height of Frustum of Cone^2+(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)
Slant Height of Frustum of Cone=Curved Surface Area of Frustum of Cone/(pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone))
Slant Height of Frustum of Cone=(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)

Can the Slant Height of Frustum of Cone given Volume be negative?

No, the Slant Height of Frustum of Cone given Volume, measured in Length cannot be negative.

Which unit is used to measure Slant Height of Frustum of Cone given Volume?

Slant Height of Frustum of Cone given Volume is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Slant Height of Frustum of Cone given Volume can be measured.

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Slant Height of Frustum of Cone given Volume Formula

​GoSlant Height of Frustum of Cone Formula

​GoSlant Height of Frustum of Cone given Curved Surface Area Formula

Slant Height of Frustum of Cone given Volume Example

Slant Height of Frustum of Cone given Volume Solution

Slant Height of Frustum of Cone given Volume Formula Elements

Other Formulas to find Slant Height of Frustum of Cone

How to Evaluate Slant Height of Frustum of Cone given Volume?

FAQs on Slant Height of Frustum of Cone given Volume

Variable Name

GoSlant Height of Frustum of Cone Formula

GoSlant Height of Frustum of Cone given Curved Surface Area Formula