Height of Cone given Lateral Surface Area Calculator

✖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%
✖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%

✖Height of Cone is defined as the distance between the apex of the Cone to the center of its circular base.ⓘ Height of Cone given Lateral Surface Area [h]

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Height of Cone given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Cone = sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2)
h = sqrt((LSA/(pi*r_Base))^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

Height of Cone - (Measured in Meter) - Height of Cone is defined as the distance between the apex of the Cone to the center of its circular base.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

h = 4.91105385450656

STEP 3: Convert Result to Output's Unit

4.91105385450656 Meter --> No Conversion Required

FINAL ANSWER

4.91105385450656 ≈ 4.911054 Meter <-- Height 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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< Height of Cone Calculators

Height of Cone given Volume and Base Circumference

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

Height of Cone given Slant Height

LaTeX Go Height of Cone = sqrt(Slant Height of Cone^2-Base Radius of Cone^2)

Height of Cone given Volume

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

Height of Cone given Volume and Base Area

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

< Height of Cone Calculators

Height of Cone given Total Surface Area

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

Height of Cone given Lateral Surface Area

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

Height of Cone given Volume

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

Height of Cone given Volume and Base Area

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

Height of Cone given Lateral Surface Area Formula

LaTeX Go

Height of Cone = sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2)
h = sqrt((LSA/(pi*r_Base))^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 Height of Cone given Lateral Surface Area?

Height of Cone given Lateral Surface Area calculator uses Height of Cone = sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2) to calculate the Height of Cone, The Height of Cone given Lateral Surface Area formula is defined as the distance between the apex of the Cone to the center of the circular base and is calculated using the lateral surface area of the Cone. Height of Cone is denoted by h symbol.

How to calculate Height of Cone given Lateral Surface Area using this online calculator? To use this online calculator for Height of Cone given Lateral Surface Area, enter Lateral Surface Area of Cone (LSA) & Base Radius of Cone (r_Base) and hit the calculate button. Here is how the Height of Cone given Lateral Surface Area calculation can be explained with given input values -> 4.911054 = sqrt((350/(pi*10))^2-10^2).

FAQ

What is Height of Cone given Lateral Surface Area?

The Height of Cone given Lateral Surface Area formula is defined as the distance between the apex of the Cone to the center of the circular base and is calculated using the lateral surface area of the Cone and is represented as h = sqrt((LSA/(pi*r_Base))^2-r_Base^2) or Height of Cone = sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2). 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 is defined as the distance between the center and any point on the circumference of the base circular surface of the Cone.

How to calculate Height of Cone given Lateral Surface Area?

The Height of Cone given Lateral Surface Area formula is defined as the distance between the apex of the Cone to the center of the circular base and is calculated using the lateral surface area of the Cone is calculated using Height of Cone = sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2). To calculate Height of Cone given Lateral Surface Area, you need Lateral Surface Area of Cone (LSA) & Base Radius of Cone (r_Base). With our tool, you need to enter the respective value for Lateral Surface Area of Cone & Base Radius 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 Height of Cone?

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

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

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