Volume of Cone given Lateral Surface Area 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%
✖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 [LSA]			+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 given Lateral Surface Area [V]

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Volume of Cone given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
V = (pi*r_Base^2*sqrt((LSA/(pi*r_Base))^2-r_Base^2))/3
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

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Base Radius of Cone: 10 Meter --> 10 Meter No Conversion Required
Lateral Surface Area of Cone: 350 Square Meter --> 350 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (pi*r_Base^2*sqrt((LSA/(pi*r_Base))^2-r_Base^2))/3 --> (pi*10^2*sqrt((350/(pi*10))^2-10^2))/3

Evaluating ... ...

V = 514.284357023389

STEP 3: Convert Result to Output's Unit

514.284357023389 Cubic Meter --> No Conversion Required

FINAL ANSWER

514.284357023389 ≈ 514.2844 Cubic Meter <-- Volume 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

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Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

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< Volume of Cone Calculators

Volume of Cone given Slant Height and Height

LaTeX Go Volume of Cone = (pi*(Slant Height of Cone^2-Height of Cone^2)*Height of Cone)/3

Volume of Cone given Base Circumference

LaTeX Go Volume of Cone = (Base Circumference of Cone^2*Height of Cone)/(12*pi)

Volume of Cone

LaTeX Go Volume of Cone = (pi*Base Radius of Cone^2*Height of Cone)/3

Volume of Cone given Base Area

LaTeX Go Volume of Cone = (Base Area of Cone*Height of Cone)/3

< Volume of Cone Calculators

Volume of Cone given Total Surface Area

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

Volume of Cone given Slant Height and Height

LaTeX Go Volume of Cone = (pi*(Slant Height of Cone^2-Height of Cone^2)*Height of Cone)/3

Volume of Cone given Base Circumference

LaTeX Go Volume of Cone = (Base Circumference of Cone^2*Height of Cone)/(12*pi)

Volume of Cone

LaTeX Go Volume of Cone = (pi*Base Radius of Cone^2*Height of Cone)/3

Volume of Cone given Lateral Surface Area Formula

LaTeX Go

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
V = (pi*r_Base^2*sqrt((LSA/(pi*r_Base))^2-r_Base^2))/3

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 Volume of Cone given Lateral Surface Area?

Volume of Cone given Lateral Surface Area calculator 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 calculate 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 calculate Volume of Cone given Lateral Surface Area using this online calculator? To use this online calculator 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. Here is how the Volume of Cone given Lateral Surface Area calculation can be explained with given input values -> 514.2844 = (pi*10^2*sqrt((350/(pi*10))^2-10^2))/3.

FAQ

What is Volume of Cone given Lateral Surface Area?

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 and is represented as V = (pi*r_Base^2*sqrt((LSA/(pi*r_Base))^2-r_Base^2))/3 or 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. 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 & Lateral Surface Area of Cone is defined as the total quantity of plane enclosed on the lateral curved surface of the Cone.

How to calculate Volume of Cone given Lateral Surface Area?

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 is calculated using 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 calculate Volume of Cone given Lateral Surface Area, you need Base Radius of Cone (r_Base) & Lateral Surface Area of Cone (LSA). With our tool, you need to enter the respective value for Base Radius of Cone & Lateral Surface Area 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 Volume of Cone?

In this formula, Volume of Cone uses Base Radius of Cone & Lateral Surface Area of Cone. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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