Slant Height of Cone given Volume and Base Area Solution

STEP 0: Pre-Calculation Summary
Formula Used
Slant Height of Cone = sqrt(((3*Volume of Cone)/Base Area of Cone)^2+Base Area of Cone/pi)
hSlant = sqrt(((3*V)/ABase)^2+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
Slant Height of Cone - (Measured in Meter) - Slant Height of Cone is the length of the line segment joining the apex of the Cone to any point on the circumference of the circular base 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.
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
Volume of Cone: 520 Cubic Meter --> 520 Cubic 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
hSlant = sqrt(((3*V)/ABase)^2+ABase/pi) --> sqrt(((3*520)/315)^2+315/pi)
Evaluating ... ...
hSlant = 11.1711096693838
STEP 3: Convert Result to Output's Unit
11.1711096693838 Meter --> No Conversion Required
FINAL ANSWER
11.1711096693838 11.17111 Meter <-- Slant Height of Cone
(Calculation completed in 00.020 seconds)

Credits

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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13 Slant Height of Cone Calculators

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

Slant Height of Cone given Volume and Base Area Formula

Slant Height of Cone = sqrt(((3*Volume of Cone)/Base Area of Cone)^2+Base Area of Cone/pi)
hSlant = sqrt(((3*V)/ABase)^2+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 Slant Height of Cone given Volume and Base Area?

Slant Height of Cone given Volume and Base Area calculator uses Slant Height of Cone = sqrt(((3*Volume of Cone)/Base Area of Cone)^2+Base Area of Cone/pi) to calculate the Slant Height of Cone, The Slant Height of Cone given Volume and Base Area formula is defined as the length of the line segment joining the apex of the Cone to any point on the circumference of the circular base of the Cone, and calculated using the volume and base area of the Cone. Slant Height of Cone is denoted by hSlant symbol.

How to calculate Slant Height of Cone given Volume and Base Area using this online calculator? To use this online calculator for Slant Height of Cone given Volume and Base Area, enter Volume of Cone (V) & Base Area of Cone (ABase) and hit the calculate button. Here is how the Slant Height of Cone given Volume and Base Area calculation can be explained with given input values -> 11.17111 = sqrt(((3*520)/315)^2+315/pi).

FAQ

What is Slant Height of Cone given Volume and Base Area?
The Slant Height of Cone given Volume and Base Area formula is defined as the length of the line segment joining the apex of the Cone to any point on the circumference of the circular base of the Cone, and calculated using the volume and base area of the Cone and is represented as hSlant = sqrt(((3*V)/ABase)^2+ABase/pi) or Slant Height of Cone = sqrt(((3*Volume of Cone)/Base Area of Cone)^2+Base Area of Cone/pi). Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire 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 Slant Height of Cone given Volume and Base Area?
The Slant Height of Cone given Volume and Base Area formula is defined as the length of the line segment joining the apex of the Cone to any point on the circumference of the circular base of the Cone, and calculated using the volume and base area of the Cone is calculated using Slant Height of Cone = sqrt(((3*Volume of Cone)/Base Area of Cone)^2+Base Area of Cone/pi). To calculate Slant Height of Cone given Volume and Base Area, you need Volume of Cone (V) & Base Area of Cone (ABase). With our tool, you need to enter the respective value for Volume 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 Slant Height of Cone?
In this formula, Slant Height of Cone uses Volume of Cone & Base Area of Cone. We can use 12 other way(s) to calculate the same, which is/are as follows -
  • Slant Height of Cone = Lateral Surface Area of Cone/(pi*Base Radius of Cone)
  • Slant Height of Cone = Total Surface Area of Cone/(pi*Base Radius of Cone)-Base Radius of Cone
  • Slant Height of Cone = sqrt(Height of Cone^2+Base Radius of Cone^2)
  • Slant Height of Cone = sqrt(((3*Volume of Cone)/(pi*Base Radius of Cone^2))^2+Base Radius of Cone^2)
  • Slant Height of Cone = sqrt(Height of Cone^2+Base Area of Cone/pi)
  • Slant Height of Cone = sqrt(Height of Cone^2+(Base Circumference of Cone/(2*pi))^2)
  • Slant Height of Cone = sqrt(((3*Volume of Cone)/(Base Circumference of Cone^2/(4*pi)))^2+(Base Circumference of Cone/(2*pi))^2)
  • Slant Height of Cone = sqrt(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone))
  • Slant Height of Cone = Lateral Surface Area of Cone/sqrt(pi*Base Area of Cone)
  • Slant Height of Cone = (2*Lateral Surface Area of Cone)/Base Circumference of Cone
  • Slant Height of Cone = Total Surface Area of Cone/sqrt(pi*Base Area of Cone)-sqrt(Base Area of Cone/pi)
  • Slant Height of Cone = (2*Total Surface Area of Cone)/Base Circumference of Cone-Base Circumference of Cone/(2*pi)
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