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Slant Height of Frustum of Cone given Volume and Base Area Formula

GoSlant Height of Frustum of Cone given Base Area Formula

GoSlant Height of Frustum of Cone given Base Area and Top 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} + \frac{A Base}{π} + (r Top \cdot \sqrt{\frac{A Base}{π}}))})}^{2} + {(r Top - \sqrt{\frac{A Base}{π}})}^{2}}

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

Slant Height of Frustum of Cone given Volume and Base Area Example

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

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

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

9.5305 = \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}}

9.5305m = \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}}

9.5305 = \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}}

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Slant Height of Frustum of Cone given Volume and Base Area Solution

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

FIRST Step Consider the formula

h Slant = \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}}

Next Step Substitute values of Variables

∴

h Slant = \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}}

Next Step Substitute values of Constants

∴

h Slant = \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}}

Next Step Prepare to Evaluate

∴

h Slant = \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}}

Next Step Evaluate

∴

h Slant = 9.5305314751646m

LAST Step Rounding Answer

∴

h Slant = 9.5305m

Slant Height of Frustum of Cone given Volume and Base Area 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 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

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 given Base Area

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

Go Slant Height of Frustum of Cone given Base Area and Top Area

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

Go Slant Height of Frustum of Cone given Top Area

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

Go Slant Height of Frustum of Cone given Curved Surface Area and Base Area

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

How to Evaluate Slant Height of Frustum of Cone given Volume and Base Area?

Slant Height of Frustum of Cone given Volume and Base Area evaluator uses Slant Height of Frustum of Cone = 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) to evaluate the Slant Height of Frustum of Cone, The Slant Height of Frustum of Cone given Volume and Base Area 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, base area and top radius 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 and Base Area using this online evaluator? To use this online evaluator for Slant Height of Frustum of Cone given Volume and Base Area, enter Volume of Frustum of Cone (V), Top Radius of Frustum of Cone (r_Top) & Base Area of Frustum of Cone (A_Base) and hit the calculate button.

FAQs on Slant Height of Frustum of Cone given Volume and Base Area

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

The formula of Slant Height of Frustum of Cone given Volume and Base Area 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 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). Here is an example- 9.530531 = sqrt(((3*1500)/(pi*(10^2+80/pi+(10*sqrt(80/pi)))))^2+(10-sqrt(80/pi))^2).

How to calculate Slant Height of Frustum of Cone given Volume and Base Area?

With Volume of Frustum of Cone (V), Top Radius of Frustum of Cone (r_Top) & Base Area of Frustum of Cone (A_Base) we can find Slant Height of Frustum of Cone given Volume and Base Area 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 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). 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-sqrt(Base Area of Frustum of Cone/pi))^2)
Slant Height of Frustum of Cone=sqrt(Height of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2)
Slant Height of Frustum of Cone=sqrt(Height of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2)

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

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

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

Slant Height of Frustum of Cone given Volume and Base Area 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 and Base Area can be measured.

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Slant Height of Frustum of Cone given Volume and Base Area Formula

​GoSlant Height of Frustum of Cone given Base Area Formula

​GoSlant Height of Frustum of Cone given Base Area and Top Area Formula

Slant Height of Frustum of Cone given Volume and Base Area Example

Slant Height of Frustum of Cone given Volume and Base Area Solution

Slant Height of Frustum of Cone given Volume and Base Area Formula Elements

Other Formulas to find Slant Height of Frustum of Cone

How to Evaluate Slant Height of Frustum of Cone given Volume and Base Area?

FAQs on Slant Height of Frustum of Cone given Volume and Base Area

Variable Name

GoSlant Height of Frustum of Cone given Base Area Formula

GoSlant Height of Frustum of Cone given Base Area and Top Area Formula