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Volume of Cone given Lateral Surface Area and Base Area Formula

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GoVolume of Cone given Base Area 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{A Base \cdot \sqrt{\frac{{LSA}^{2}}{π \cdot A Base} - \frac{A Base}{π}}}{3}

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

Volume of Cone given Lateral Surface Area and Base Area Example

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

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

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

509.2182 = \frac{315 \cdot \sqrt{\frac{350^{2}}{3.1416 \cdot 315} - \frac{315}{3.1416}}}{3}

509.2182m³ = \frac{315m² \cdot \sqrt{\frac{{350m²}^{2}}{3.1416 \cdot 315m²} - \frac{315m²}{3.1416}}}{3}

509.2182 = \frac{315 \cdot \sqrt{\frac{350^{2}}{3.1416 \cdot 315} - \frac{315}{3.1416}}}{3}

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Volume of Cone given Lateral Surface Area and Base Area Solution

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

FIRST Step Consider the formula

V = \frac{A Base \cdot \sqrt{\frac{{LSA}^{2}}{π \cdot A Base} - \frac{A Base}{π}}}{3}

Next Step Substitute values of Variables

∴

V = \frac{315m² \cdot \sqrt{\frac{{350m²}^{2}}{π \cdot 315m²} - \frac{315m²}{π}}}{3}

Next Step Substitute values of Constants

∴

V = \frac{315m² \cdot \sqrt{\frac{{350m²}^{2}}{3.1416 \cdot 315m²} - \frac{315m²}{3.1416}}}{3}

Next Step Prepare to Evaluate

∴

V = \frac{315 \cdot \sqrt{\frac{350^{2}}{3.1416 \cdot 315} - \frac{315}{3.1416}}}{3}

Next Step Evaluate

∴

V = 509.218215534824m³

LAST Step Rounding Answer

∴

V = 509.2182m³

Volume of Cone given Lateral Surface Area and Base 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 Area of Cone

Base Area of Cone is the total quantity of plane enclosed on the base circular surface of the Cone.

Symbol: A_Base

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Base Area 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 Area

V = \frac{A Base \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}

How to Evaluate Volume of Cone given Lateral Surface Area and Base Area?

Volume of Cone given Lateral Surface Area and Base Area evaluator uses Volume of Cone = (Base Area of Cone*sqrt(Lateral Surface Area of Cone^2/(pi*Base Area of Cone)-Base Area of Cone/pi))/3 to evaluate the Volume of Cone, The Volume of Cone given Lateral Surface Area and Base 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 and base area of the Cone. Volume of Cone is denoted by V symbol.

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

FAQs on Volume of Cone given Lateral Surface Area and Base Area

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

The formula of Volume of Cone given Lateral Surface Area and Base Area is expressed as Volume of Cone = (Base Area of Cone*sqrt(Lateral Surface Area of Cone^2/(pi*Base Area of Cone)-Base Area of Cone/pi))/3. Here is an example- 509.2182 = (315*sqrt(350^2/(pi*315)-315/pi))/3.

How to calculate Volume of Cone given Lateral Surface Area and Base Area?

With Base Area of Cone (A_Base) & Lateral Surface Area of Cone (LSA) we can find Volume of Cone given Lateral Surface Area and Base Area using the formula - Volume of Cone = (Base Area of Cone*sqrt(Lateral Surface Area of Cone^2/(pi*Base Area of Cone)-Base Area of Cone/pi))/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 Area of Cone*Height of Cone)/3
Volume of Cone=(Base Circumference of Cone^2*Height of Cone)/(12*pi)

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

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

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

Volume of Cone given Lateral Surface Area and Base 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 and Base Area can be measured.

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Volume of Cone given Lateral Surface Area and Base Area Formula

​GoVolume of Cone Formula

​GoVolume of Cone given Base Area Formula

Volume of Cone given Lateral Surface Area and Base Area Example

Volume of Cone given Lateral Surface Area and Base Area Solution

Volume of Cone given Lateral Surface Area and Base Area Formula Elements

Other Formulas to find Volume of Cone

How to Evaluate Volume of Cone given Lateral Surface Area and Base Area?

FAQs on Volume of Cone given Lateral Surface Area and Base Area

Variable Name

GoVolume of Cone Formula

GoVolume of Cone given Base Area Formula