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Volume of Cone given Lateral Surface Area Formula

GoVolume of Cone Formula

GoVolume of Cone given Base Circumference Formula

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Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone. Check FAQs

V = \frac{π \cdot {r Base}^{2} \cdot \sqrt{{(\frac{LSA}{π \cdot r Base})}^{2} - {r Base}^{2}}}{3}

V - Volume of Cone?r_Base - Base Radius of Cone?LSA - Lateral Surface Area of Cone?π - Archimedes' constant?

Volume of Cone given Lateral Surface Area Example

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

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

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

514.2844 = \frac{3.1416 \cdot 10^{2} \cdot \sqrt{{(\frac{350}{3.1416 \cdot 10})}^{2} - 10^{2}}}{3}

514.2844m³ = \frac{3.1416 \cdot {10m}^{2} \cdot \sqrt{{(\frac{350m²}{3.1416 \cdot 10m})}^{2} - {10m}^{2}}}{3}

514.2844 = \frac{3.1416 \cdot 10^{2} \cdot \sqrt{{(\frac{350}{3.1416 \cdot 10})}^{2} - 10^{2}}}{3}

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Volume of Cone given Lateral Surface Area Solution

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

FIRST Step Consider the formula

V = \frac{π \cdot {r Base}^{2} \cdot \sqrt{{(\frac{LSA}{π \cdot r Base})}^{2} - {r Base}^{2}}}{3}

Next Step Substitute values of Variables

∴

V = \frac{π \cdot {10m}^{2} \cdot \sqrt{{(\frac{350m²}{π \cdot 10m})}^{2} - {10m}^{2}}}{3}

Next Step Substitute values of Constants

∴

V = \frac{3.1416 \cdot {10m}^{2} \cdot \sqrt{{(\frac{350m²}{3.1416 \cdot 10m})}^{2} - {10m}^{2}}}{3}

Next Step Prepare to Evaluate

∴

V = \frac{3.1416 \cdot 10^{2} \cdot \sqrt{{(\frac{350}{3.1416 \cdot 10})}^{2} - 10^{2}}}{3}

Next Step Evaluate

∴

V = 514.284357023389m³

LAST Step Rounding Answer

∴

V = 514.2844m³

Volume of Cone given Lateral Surface Area Formula Elements

Variables

Constants

Functions

Volume of Cone

Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume 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

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

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 Volume of Cone

Go Volume of Cone

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

Go Volume of Cone given Base Circumference

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

Go Volume of Cone given Slant Height and Height

V = \frac{π \cdot ({h Slant}^{2} - h^{2}) \cdot h}{3}

Go Volume of Cone given Total Surface Area

V = \frac{π \cdot {r Base}^{2} \cdot \sqrt{{(\frac{TSA}{π \cdot r Base} - r Base)}^{2} - {r Base}^{2}}}{3}

How to Evaluate Volume of Cone given Lateral Surface Area?

Volume of Cone given Lateral Surface Area evaluator uses Volume of Cone = (pi*Base Radius of Cone^2*sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2))/3 to evaluate the Volume of Cone, The Volume of Cone given Lateral Surface Area formula is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone, and calculated using the lateral surface area of the Cone. Volume of Cone is denoted by V symbol.

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

FAQs on Volume of Cone given Lateral Surface Area

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

The formula of Volume of Cone given Lateral Surface Area is expressed as Volume of Cone = (pi*Base Radius of Cone^2*sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2))/3. Here is an example- 514.2844 = (pi*10^2*sqrt((350/(pi*10))^2-10^2))/3.

How to calculate Volume of Cone given Lateral Surface Area?

With Base Radius of Cone (r_Base) & Lateral Surface Area of Cone (LSA) we can find Volume of Cone given Lateral Surface Area using the formula - Volume of Cone = (pi*Base Radius of Cone^2*sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2))/3. This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Cone?

Here are the different ways to Calculate Volume of Cone-

Volume of Cone=(pi*Base Radius of Cone^2*Height of Cone)/3
Volume of Cone=(Base Circumference of Cone^2*Height of Cone)/(12*pi)
Volume of Cone=(pi*(Slant Height of Cone^2-Height of Cone^2)*Height of Cone)/3

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

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

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

Volume of Cone given Lateral Surface Area is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Cone given Lateral Surface Area can be measured.

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Volume of Cone given Lateral Surface Area Formula

​GoVolume of Cone Formula

​GoVolume of Cone given Base Circumference Formula

Volume of Cone given Lateral Surface Area Example

Volume of Cone given Lateral Surface Area Solution

Volume of Cone given Lateral Surface Area Formula Elements

Other Formulas to find Volume of Cone

How to Evaluate Volume of Cone given Lateral Surface Area?

FAQs on Volume of Cone given Lateral Surface Area

Variable Name

GoVolume of Cone Formula

GoVolume of Cone given Base Circumference Formula