Lateral Surface Area of Cone given Volume Calculator

✖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.ⓘ Base Radius of Cone [r_Base]			+10% -10%
✖Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone.ⓘ Volume of Cone [V]			+10% -10%

✖Lateral Surface Area of Cone is defined as the total quantity of plane enclosed on the lateral curved surface of the Cone.ⓘ Lateral Surface Area of Cone given Volume [LSA]

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Formula

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Lateral Surface Area of Cone given Volume

Formula

`"LSA" = pi*"r"_{"Base"}*sqrt(((3*"V")/(pi*"r"_{"Base"}^2))^2+"r"_{"Base"}^2)`

Example

`"350.7592m²"=pi*"10m"*sqrt(((3*"520m³")/(pi*("10m")^2))^2+("10m")^2)`

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Lateral Surface Area of Cone given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
LSA = pi*r_Base*sqrt(((3*V)/(pi*r_Base^2))^2+r_Base^2)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Lateral Surface Area of Cone - (Measured in Square Meter) - Lateral Surface Area of Cone is defined as the total quantity of plane enclosed on the lateral curved surface of the Cone.
Base Radius of Cone - (Measured in Meter) - 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.
Volume of Cone - (Measured in Cubic Meter) - Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone.

STEP 1: Convert Input(s) to Base Unit

Base Radius of Cone: 10 Meter --> 10 Meter No Conversion Required
Volume of Cone: 520 Cubic Meter --> 520 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

LSA = pi*r_Base*sqrt(((3*V)/(pi*r_Base^2))^2+r_Base^2) --> pi*10*sqrt(((3*520)/(pi*10^2))^2+10^2)

Evaluating ... ...

LSA = 350.759239380652

STEP 3: Convert Result to Output's Unit

350.759239380652 Square Meter --> No Conversion Required

FINAL ANSWER

350.759239380652 ≈ 350.7592 Square Meter <-- Lateral Surface Area of Cone

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

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

Dhruv Walia has created this Calculator and 1100+ more calculators!

Verified by Nikita Kumari

The National Institute of Engineering (NIE), Mysuru

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< 13 Lateral Surface Area of Cone Calculators

Lateral Surface Area of Cone given Volume and Height

Go Lateral Surface Area of Cone = pi*sqrt((3*Volume of Cone)/(pi*Height of Cone)*(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone)))

Lateral Surface Area of Cone given Volume and Base Circumference

Go Lateral Surface Area of Cone = Base Circumference of Cone/2*sqrt(((3*Volume of Cone)/(Base Circumference of Cone^2/(4*pi)))^2+(Base Circumference of Cone/(2*pi))^2)

Lateral Surface Area of Cone given Volume and Base Area

Go Lateral Surface Area of Cone = pi*sqrt(Base Area of Cone/pi*(((3*Volume of Cone)/Base Area of Cone)^2+Base Area of Cone/pi))

Lateral Surface Area of Cone given Volume

Go 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)

Lateral Surface Area of Cone given Height and Base Area

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

Lateral Surface Area of Cone given Height and Base Circumference

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

Lateral Surface Area of Cone given Height

Go 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 given Base Area and Slant Height

Go Lateral Surface Area of Cone = pi*sqrt(Base Area of Cone/pi)*Slant Height of Cone

Lateral Surface Area of Cone given Total Surface Area and Base Circumference

Go Lateral Surface Area of Cone = Total Surface Area of Cone-Base Circumference of Cone^2/(4*pi)

Lateral Surface Area of Cone given Total Surface Area

Go Lateral Surface Area of Cone = Total Surface Area of Cone-pi*Base Radius of Cone^2

Lateral Surface Area of Cone

Go Lateral Surface Area of Cone = pi*Base Radius of Cone*Slant Height of Cone

Lateral Surface Area of Cone given Base Circumference and Slant Height

Go Lateral Surface Area of Cone = Base Circumference of Cone/2*Slant Height of Cone

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

Go Lateral Surface Area of Cone = Total Surface Area of Cone-Base Area of Cone

< 11 Surface Area of Cone Calculators

Lateral Surface Area of Cone given Volume

Go 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)

Lateral Surface Area of Cone given Height

Go 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 given Base Area and Slant Height

Go Lateral Surface Area of Cone = pi*sqrt(Base Area of Cone/pi)*Slant Height of Cone

Total Surface Area of Cone

Go Total Surface Area of Cone = pi*Base Radius of Cone*(Base Radius of Cone+Slant Height of Cone)

Total Surface Area of Cone given Base Area

Go Total Surface Area of Cone = (pi*Base Radius of Cone*Slant Height of Cone)+Base Area of Cone

Base Area of Cone given Lateral Surface Area and Slant Height

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

Total Surface Area of Cone given Lateral Surface Area

Go Total Surface Area of Cone = Lateral Surface Area of Cone+(pi*Base Radius of Cone^2)

Lateral Surface Area of Cone

Go Lateral Surface Area of Cone = pi*Base Radius of Cone*Slant Height of Cone

Lateral Surface Area of Cone given Base Circumference and Slant Height

Go Lateral Surface Area of Cone = Base Circumference of Cone/2*Slant Height of Cone

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

Go Total Surface Area of Cone = Lateral Surface Area of Cone+Base Area of Cone

Base Area of Cone

Go Base Area of Cone = pi*Base Radius of Cone^2

Lateral Surface Area of Cone given Volume 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)
LSA = pi*r_Base*sqrt(((3*V)/(pi*r_Base^2))^2+r_Base^2)

What is a Cone?

A Cone is obtained by rotating a line inclined at a fixed acute angle from a fixed axis of rotation. The sharp tip is called the apex of the Cone. If the rotating line is crossing the axis of rotation, then the resulting shape is a double-napped Cone - two oppositely placed Cones joined on the apex. Cutting a Cone by a plane will result in some important two-dimensional shapes like circles, ellipses, parabolas, and hyperbolas, depending on the angle of cutting.

How to Calculate Lateral Surface Area of Cone given Volume?

Lateral Surface Area of Cone given Volume calculator 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 calculate 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 calculate Lateral Surface Area of Cone given Volume using this online calculator? To use this online calculator for Lateral Surface Area of Cone given Volume, enter Base Radius of Cone (r_Base) & Volume of Cone (V) and hit the calculate button. Here is how the Lateral Surface Area of Cone given Volume calculation can be explained with given input values -> 350.7592 = pi*10*sqrt(((3*520)/(pi*10^2))^2+10^2).

FAQ

What is Lateral Surface Area of Cone given Volume?

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 and is represented as LSA = pi*r_Base*sqrt(((3*V)/(pi*r_Base^2))^2+r_Base^2) or 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). 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 & Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone.

How to calculate Lateral Surface Area of Cone given Volume?

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 is calculated using 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 calculate Lateral Surface Area of Cone given Volume, you need Base Radius of Cone (r_Base) & Volume of Cone (V). With our tool, you need to enter the respective value for Base Radius of Cone & Volume of Cone and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Lateral Surface Area of Cone?

In this formula, Lateral Surface Area of Cone uses Base Radius of Cone & Volume of Cone. We can use 16 other way(s) to calculate the same, which is/are as follows -

Lateral Surface Area of Cone = pi*sqrt(Base Area of Cone/pi)*Slant Height of Cone
Lateral Surface Area of Cone = pi*Base Radius of Cone*Slant Height of Cone
Lateral Surface Area of Cone = Base Circumference of Cone/2*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*(Height of Cone^2+Base Area of Cone/pi))
Lateral Surface Area of Cone = Base Circumference of Cone/2*sqrt(Height of Cone^2+(Base Circumference of Cone/(2*pi))^2)
Lateral Surface Area of Cone = Total Surface Area of Cone-pi*Base Radius of Cone^2
Lateral Surface Area of Cone = Total Surface Area of Cone-Base Area of Cone
Lateral Surface Area of Cone = Total Surface Area of Cone-Base Circumference of Cone^2/(4*pi)
Lateral Surface Area of Cone = pi*sqrt((3*Volume of Cone)/(pi*Height of Cone)*(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone)))
Lateral Surface Area of Cone = Base Circumference of Cone/2*sqrt(((3*Volume of Cone)/(Base Circumference of Cone^2/(4*pi)))^2+(Base Circumference of Cone/(2*pi))^2)
Lateral Surface Area of Cone = pi*sqrt(Base Area of Cone/pi*(((3*Volume of Cone)/Base Area of Cone)^2+Base Area of Cone/pi))
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
Lateral Surface Area of Cone = Base Circumference of Cone/2*Slant Height of Cone

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