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Height of Frustum of Cone given Slant Height and Top Area Formula

GoHeight of Frustum of Cone given Volume and Base Area Formula

GoHeight of Frustum of Cone given Volume and Top Area Formula

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

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

h - Height of Frustum of Cone?h_Slant - Slant Height of Frustum of Cone?A_Top - Top Area of Frustum of Cone?r_Base - Base Radius of Frustum of Cone?π - Archimedes' constant?

Height of Frustum of Cone given Slant Height and Top Area Example

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

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

7.4744 = \sqrt{9^{2} - {(\sqrt{\frac{315}{3.1416}} - 5)}^{2}}

7.4744m = \sqrt{{9m}^{2} - {(\sqrt{\frac{315m²}{3.1416}} - 5m)}^{2}}

7.4744 = \sqrt{9^{2} - {(\sqrt{\frac{315}{3.1416}} - 5)}^{2}}

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Height of Frustum of Cone given Slant Height and Top Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = \sqrt{{9m}^{2} - {(\sqrt{\frac{315m²}{π}} - 5m)}^{2}}

Next Step Substitute values of Constants

∴

h = \sqrt{{9m}^{2} - {(\sqrt{\frac{315m²}{3.1416}} - 5m)}^{2}}

Next Step Prepare to Evaluate

∴

h = \sqrt{9^{2} - {(\sqrt{\frac{315}{3.1416}} - 5)}^{2}}

Next Step Evaluate

∴

h = 7.474363084837m

LAST Step Rounding Answer

∴

h = 7.4744m

Height of Frustum of Cone given Slant Height and Top Area Formula Elements

Variables

Constants

Functions

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

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

Top Area of Frustum of Cone

Top Area of Frustum of Cone is the total amount of two-dimensional space occupied by the top face of the Frustum of the Cone.

Symbol: A_Top

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Top Area 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 Height of Frustum of Cone

Go Height of Frustum of Cone given Volume and Base Area

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

Go Height of Frustum of Cone given Volume and Top Area

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

Go Height of Frustum of Cone given Volume, Top Area and Base Area

h = \frac{3 \cdot V}{A Top + A Base + (\sqrt{A Top \cdot A Base})}

Go Height of Frustum of Cone given Total Surface Area and Base Area

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

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

Height of Frustum of Cone given Slant Height and Top Area evaluator uses Height of Frustum of Cone = sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2) to evaluate the Height of Frustum of Cone, The Height of Frustum of Cone given Slant Height and Top Area formula is defined as the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone and calculated using the slant height, top area, and base radius of the Frustum of Cone. Height of Frustum of Cone is denoted by h symbol.

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

FAQs on Height of Frustum of Cone given Slant Height and Top Area

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

The formula of Height of Frustum of Cone given Slant Height and Top Area is expressed as Height of Frustum of Cone = sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2). Here is an example- 7.474363 = sqrt(9^2-(sqrt(315/pi)-5)^2).

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

With Slant Height of Frustum of Cone (h_Slant), Top Area of Frustum of Cone (A_Top) & Base Radius of Frustum of Cone (r_Base) we can find Height of Frustum of Cone given Slant Height and Top Area using the formula - Height of Frustum of Cone = sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-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 Height of Frustum of Cone?

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

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

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

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

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

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

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Height of Frustum of Cone given Slant Height and Top Area Formula

​GoHeight of Frustum of Cone given Volume and Base Area Formula

​GoHeight of Frustum of Cone given Volume and Top Area Formula

Height of Frustum of Cone given Slant Height and Top Area Example

Height of Frustum of Cone given Slant Height and Top Area Solution

Height of Frustum of Cone given Slant Height and Top Area Formula Elements

Other Formulas to find Height of Frustum of Cone

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

FAQs on Height of Frustum of Cone given Slant Height and Top Area

Variable Name

GoHeight of Frustum of Cone given Volume and Base Area Formula

GoHeight of Frustum of Cone given Volume and Top Area Formula