Height of Cone given Lateral Surface Area and Base Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Height of Cone = sqrt(Lateral Surface Area of Cone^2/(pi*Base Area of Cone)-Base Area of Cone/pi)
h = sqrt(LSA^2/(pi*ABase)-ABase/pi)
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 Area of Cone - (Measured in Square Meter) - Base Area of Cone is the total quantity of plane enclosed on 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 Area of Cone: 315 Square Meter --> 315 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h = sqrt(LSA^2/(pi*ABase)-ABase/pi) --> sqrt(350^2/(pi*315)-315/pi)
Evaluating ... ...
h = 4.84969729080785
STEP 3: Convert Result to Output's Unit
4.84969729080785 Meter --> No Conversion Required
FINAL ANSWER
4.84969729080785 4.849697 Meter <-- Height of Cone
(Calculation completed in 00.004 seconds)

Credits

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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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12 Height of Cone Calculators

Height of Cone given Total Surface Area and Base Area
​ Go Height of Cone = sqrt((Total Surface Area of Cone/sqrt(pi*Base Area of Cone)-sqrt(Base Area of Cone/pi))^2-Base Area of Cone/pi)
Height of Cone given Total Surface Area and Base Circumference
​ Go Height of Cone = sqrt(((2*Total Surface Area of Cone)/Base Circumference of Cone-Base Circumference of Cone/(2*pi))^2-(Base Circumference of Cone/(2*pi))^2)
Height of Cone given Total Surface Area
​ 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 and Base Area
​ Go Height of Cone = sqrt(Lateral Surface Area of Cone^2/(pi*Base Area of Cone)-Base Area of Cone/pi)
Height of Cone given Lateral Surface Area and Base Circumference
​ Go Height of Cone = sqrt(((2*Lateral Surface Area of Cone)/Base Circumference of Cone)^2-(Base Circumference of Cone/(2*pi))^2)
Height of Cone given Lateral Surface Area
​ 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 Slant Height and Base Circumference
​ Go Height of Cone = sqrt(Slant Height of Cone^2-(Base Circumference of Cone/(2*pi))^2)
Height of Cone given Slant Height and Base Area
​ Go Height of Cone = sqrt(Slant Height of Cone^2-Base Area of Cone/pi)
Height of Cone given Volume and Base Circumference
​ Go Height of Cone = (12*pi*Volume of Cone)/(Base Circumference of Cone^2)
Height of Cone given Slant Height
​ Go Height of Cone = sqrt(Slant Height of Cone^2-Base Radius of Cone^2)
Height of Cone given Volume
​ Go Height of Cone = (3*Volume of Cone)/(pi*Base Radius of Cone^2)
Height of Cone given Volume and Base Area
​ Go Height of Cone = (3*Volume of Cone)/Base Area of Cone

Height of Cone given Lateral Surface Area and Base Area Formula

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

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 and Base Area?

Height of Cone given Lateral Surface Area and Base Area calculator uses Height of Cone = sqrt(Lateral Surface Area of Cone^2/(pi*Base Area of Cone)-Base Area of Cone/pi) to calculate the Height of Cone, The Height of Cone given Lateral Surface Area and Base 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 and base area of the Cone. Height of Cone is denoted by h symbol.

How to calculate Height of Cone given Lateral Surface Area and Base Area using this online calculator? To use this online calculator for Height of Cone given Lateral Surface Area and Base Area, enter Lateral Surface Area of Cone (LSA) & Base Area of Cone (ABase) and hit the calculate button. Here is how the Height of Cone given Lateral Surface Area and Base Area calculation can be explained with given input values -> 4.849697 = sqrt(350^2/(pi*315)-315/pi).

FAQ

What is Height of Cone given Lateral Surface Area and Base Area?
The Height of Cone given Lateral Surface Area and Base 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 and base area of the Cone and is represented as h = sqrt(LSA^2/(pi*ABase)-ABase/pi) or Height of Cone = sqrt(Lateral Surface Area of Cone^2/(pi*Base Area of Cone)-Base Area of Cone/pi). Lateral Surface Area of Cone is defined as the total quantity of plane enclosed on the lateral curved surface of the Cone & Base Area of Cone is the total quantity of plane enclosed on the base circular surface of the Cone.
How to calculate Height of Cone given Lateral Surface Area and Base Area?
The Height of Cone given Lateral Surface Area and Base 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 and base area of the Cone is calculated using Height of Cone = sqrt(Lateral Surface Area of Cone^2/(pi*Base Area of Cone)-Base Area of Cone/pi). To calculate Height of Cone given Lateral Surface Area and Base Area, you need Lateral Surface Area of Cone (LSA) & Base Area of Cone (ABase). With our tool, you need to enter the respective value for Lateral Surface Area of Cone & Base 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 Height of Cone?
In this formula, Height of Cone uses Lateral Surface Area of Cone & Base Area of Cone. We can use 11 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
  • Height of Cone = (12*pi*Volume of Cone)/(Base Circumference of Cone^2)
  • Height of Cone = sqrt(Slant Height of Cone^2-Base Area of Cone/pi)
  • Height of Cone = sqrt(Slant Height of Cone^2-(Base Circumference of Cone/(2*pi))^2)
  • Height of Cone = sqrt((Lateral Surface Area of Cone/(pi*Base Radius of Cone))^2-Base Radius of Cone^2)
  • Height of Cone = sqrt(((2*Lateral Surface Area of Cone)/Base Circumference of Cone)^2-(Base Circumference of Cone/(2*pi))^2)
  • 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 = sqrt((Total Surface Area of Cone/sqrt(pi*Base Area of Cone)-sqrt(Base Area of Cone/pi))^2-Base Area of Cone/pi)
  • Height of Cone = sqrt(((2*Total Surface Area of Cone)/Base Circumference of Cone-Base Circumference of Cone/(2*pi))^2-(Base Circumference of Cone/(2*pi))^2)
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