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Lateral Surface Area of Cone given Volume Formula

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GoLateral Surface Area of Cone given Height Formula

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

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

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

Lateral Surface Area of Cone given Volume Example

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

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

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

350.7592 = 3.1416 \cdot 10 \cdot \sqrt{{(\frac{3 \cdot 520}{3.1416 \cdot 10^{2}})}^{2} + 10^{2}}

350.7592m² = 3.1416 \cdot 10m \cdot \sqrt{{(\frac{3 \cdot 520m³}{3.1416 \cdot {10m}^{2}})}^{2} + {10m}^{2}}

350.7592 = 3.1416 \cdot 10 \cdot \sqrt{{(\frac{3 \cdot 520}{3.1416 \cdot 10^{2}})}^{2} + 10^{2}}

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Home » Math » Geometry » 3D Geometry » Lateral Surface Area of Cone given Volume

Lateral Surface Area of Cone given Volume Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

LSA = π \cdot 10m \cdot \sqrt{{(\frac{3 \cdot 520m³}{π \cdot {10m}^{2}})}^{2} + {10m}^{2}}

Next Step Substitute values of Constants

∴

LSA = 3.1416 \cdot 10m \cdot \sqrt{{(\frac{3 \cdot 520m³}{3.1416 \cdot {10m}^{2}})}^{2} + {10m}^{2}}

Next Step Prepare to Evaluate

∴

LSA = 3.1416 \cdot 10 \cdot \sqrt{{(\frac{3 \cdot 520}{3.1416 \cdot 10^{2}})}^{2} + 10^{2}}

Next Step Evaluate

∴

LSA = 350.759239380652m²

LAST Step Rounding Answer

∴

LSA = 350.7592m²

Lateral Surface Area of Cone given Volume Formula Elements

Variables

Constants

Functions

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.

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.

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.

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)

Credits

Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has created this Formula and 1100+ more formulas!

Verified by Nikita Salampuria

The National Institute of Engineering (NIE), Mysuru

Nikita Salampuria has verified this Formula and 600+ more formulas!

Other Formulas to find Lateral Surface Area of Cone

Go Lateral Surface Area of Cone

LSA = π \cdot r Base \cdot h Slant

Go Lateral Surface Area of Cone given Height

LSA = π \cdot r Base \cdot \sqrt{h^{2} + {r Base}^{2}}

Go Lateral Surface Area of Cone given Base Area and Slant Height

LSA = π \cdot \sqrt{\frac{A Base}{π}} \cdot h Slant

Go Lateral Surface Area of Cone given Base Circumference and Slant Height

LSA = \frac{C Base}{2} \cdot h Slant

Other formulas in Lateral Surface Area of Cone category

Go Base Area of Cone

A Base = π \cdot {r Base}^{2}

Go Base Area of Cone given Lateral Surface Area and Slant Height

A Base = π \cdot {(\frac{LSA}{π \cdot h Slant})}^{2}

Go Total Surface Area of Cone

TSA = π \cdot r Base \cdot (r Base + h Slant)

Go Total Surface Area of Cone given Base Area

TSA = (π \cdot r Base \cdot h Slant) + A Base

How to Evaluate Lateral Surface Area of Cone given Volume?

Lateral Surface Area of Cone given Volume evaluator uses Lateral Surface Area of Cone = pi*Base Radius of Cone*sqrt(((3*Volume of Cone)/(pi*Base Radius of Cone^2))^2+Base Radius of Cone^2) to evaluate the Lateral Surface Area of Cone, The Lateral Surface Area of Cone given Volume formula is defined as the total quantity of plane enclosed on the lateral curved surface of the Cone and is calculated using the volume of the Cone. Lateral Surface Area of Cone is denoted by LSA symbol.

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

FAQs on Lateral Surface Area of Cone given Volume

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

The formula of Lateral Surface Area of Cone given Volume is expressed as Lateral Surface Area of Cone = pi*Base Radius of Cone*sqrt(((3*Volume of Cone)/(pi*Base Radius of Cone^2))^2+Base Radius of Cone^2). Here is an example- 350.7592 = pi*10*sqrt(((3*520)/(pi*10^2))^2+10^2).

How to calculate Lateral Surface Area of Cone given Volume?

With Base Radius of Cone (r_Base) & Volume of Cone (V) we can find Lateral Surface Area of Cone given Volume using the formula - Lateral Surface Area of Cone = pi*Base Radius of Cone*sqrt(((3*Volume of Cone)/(pi*Base Radius of Cone^2))^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 Lateral Surface Area of Cone?

Here are the different ways to Calculate Lateral Surface Area of Cone-

Lateral Surface Area of Cone=pi*Base Radius of Cone*Slant Height of Cone
Lateral Surface Area of Cone=pi*Base Radius of Cone*sqrt(Height of Cone^2+Base Radius of Cone^2)
Lateral Surface Area of Cone=pi*sqrt(Base Area of Cone/pi)*Slant Height of Cone

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

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

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

Lateral Surface Area of Cone given Volume is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Lateral Surface Area of Cone given Volume can be measured.

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Lateral Surface Area of Cone given Volume Formula

​GoLateral Surface Area of Cone Formula

​GoLateral Surface Area of Cone given Height Formula

Lateral Surface Area of Cone given Volume Example

Lateral Surface Area of Cone given Volume Solution

Lateral Surface Area of Cone given Volume Formula Elements

Credits

Other Formulas to find Lateral Surface Area of Cone

Other formulas in Lateral Surface Area of Cone category

How to Evaluate Lateral Surface Area of Cone given Volume?

FAQs on Lateral Surface Area of Cone given Volume

Variable Name

GoLateral Surface Area of Cone Formula

GoLateral Surface Area of Cone given Height Formula