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Height of Cone given Lateral Surface Area Formula

GoHeight of Cone given Total Surface Area Formula

GoHeight of Cone given Volume Formula

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Height of Cone is defined as the distance between the apex of the Cone to the center of its circular base. Check FAQs

h = \sqrt{{(\frac{LSA}{π \cdot r Base})}^{2} - {r Base}^{2}}

h - Height of Cone?LSA - Lateral Surface Area of Cone?r_Base - Base Radius of Cone?π - Archimedes' constant?

Height of Cone given Lateral Surface Area Example

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Here is how the Height of Cone given Lateral Surface Area equation looks like with Values.

Here is how the Height of Cone given Lateral Surface Area equation looks like with Units.

Here is how the Height of Cone given Lateral Surface Area equation looks like.

4.9111 = \sqrt{{(\frac{350}{3.1416 \cdot 10})}^{2} - 10^{2}}

4.9111m = \sqrt{{(\frac{350m²}{3.1416 \cdot 10m})}^{2} - {10m}^{2}}

4.9111 = \sqrt{{(\frac{350}{3.1416 \cdot 10})}^{2} - 10^{2}}

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Height of Cone given Lateral Surface Area Solution

Follow our step by step solution on how to calculate Height of Cone given Lateral Surface Area?

FIRST Step Consider the formula

h = \sqrt{{(\frac{LSA}{π \cdot r Base})}^{2} - {r Base}^{2}}

Next Step Substitute values of Variables

∴

h = \sqrt{{(\frac{350m²}{π \cdot 10m})}^{2} - {10m}^{2}}

Next Step Substitute values of Constants

∴

h = \sqrt{{(\frac{350m²}{3.1416 \cdot 10m})}^{2} - {10m}^{2}}

Next Step Prepare to Evaluate

∴

h = \sqrt{{(\frac{350}{3.1416 \cdot 10})}^{2} - 10^{2}}

Next Step Evaluate

∴

h = 4.91105385450656m

LAST Step Rounding Answer

∴

h = 4.9111m

Height of Cone given Lateral Surface Area Formula Elements

Variables

Constants

Functions

Height of Cone

Height of Cone is defined as the distance between the apex of the Cone to the center of its circular base.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Cone

Lateral Surface Area of Cone

Lateral Surface Area of Cone is defined as the total quantity of plane enclosed on the lateral curved surface of the Cone.

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral Surface Area of Cone

Base Radius of Cone

Base Radius of Cone is defined as the distance between the center and any point on the circumference of the base circular surface of the Cone.

Symbol: r_Base

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Base Radius 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 Cone

Go Height of Cone given Total Surface Area

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

Go Height of Cone given Volume

h = \frac{3 \cdot V}{π \cdot {r Base}^{2}}

Go Height of Cone given Volume and Base Area

h = \frac{3 \cdot V}{A Base}

Go Height of Cone given Volume and Base Circumference

h = \frac{12 \cdot π \cdot V}{{C Base}^{2}}

How to Evaluate Height of Cone given Lateral Surface Area?

Height of Cone given Lateral Surface Area evaluator uses Height of Cone = sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2) to evaluate the Height of Cone, The Height of Cone given Lateral Surface Area formula is defined as the distance between the apex of the Cone to the center of the circular base and is calculated using the lateral surface area of the Cone. Height of Cone is denoted by h symbol.

How to evaluate Height of Cone given Lateral Surface Area using this online evaluator? To use this online evaluator for Height of Cone given Lateral Surface Area, enter Lateral Surface Area of Cone (LSA) & Base Radius of Cone (r_Base) and hit the calculate button.

FAQs on Height of Cone given Lateral Surface Area

What is the formula to find Height of Cone given Lateral Surface Area?

The formula of Height of Cone given Lateral Surface Area is expressed as Height of Cone = sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2). Here is an example- 4.911054 = sqrt((350/(pi*10))^2-10^2).

How to calculate Height of Cone given Lateral Surface Area?

With Lateral Surface Area of Cone (LSA) & Base Radius of Cone (r_Base) we can find Height of Cone given Lateral Surface Area using the formula - Height of Cone = sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Height of Cone?

Here are the different ways to Calculate Height of Cone-

Height of Cone=sqrt((Total Surface Area of Cone/(pi*Base Radius of Cone)-Base Radius of Cone)^2-Base Radius of Cone^2)
Height of Cone=(3*Volume of Cone)/(pi*Base Radius of Cone^2)
Height of Cone=(3*Volume of Cone)/Base Area of Cone

Can the Height of Cone given Lateral Surface Area be negative?

No, the Height of Cone given Lateral Surface Area, measured in Length cannot be negative.

Which unit is used to measure Height of Cone given Lateral Surface Area?

Height of Cone given Lateral Surface 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 Cone given Lateral Surface Area can be measured.

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Height of Cone given Lateral Surface Area Formula

​GoHeight of Cone given Total Surface Area Formula

​GoHeight of Cone given Volume Formula

Height of Cone given Lateral Surface Area Example

Height of Cone given Lateral Surface Area Solution

Height of Cone given Lateral Surface Area Formula Elements

Other Formulas to find Height of Cone

How to Evaluate Height of Cone given Lateral Surface Area?

FAQs on Height of Cone given Lateral Surface Area

Variable Name

GoHeight of Cone given Total Surface Area Formula

GoHeight of Cone given Volume Formula