Slant Height of Cone given Volume and Height Calculator

✖Height of Cone is defined as the distance between the apex of the Cone to the center of its circular base.ⓘ Height of Cone [h]			+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%

✖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.ⓘ Slant Height of Cone given Volume and Height [h_Slant]

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Slant Height of Cone given Volume and Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slant Height of Cone = sqrt(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone))
h_Slant = sqrt(h^2+(3*V)/(pi*h))
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.
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.
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

Height of Cone: 5 Meter --> 5 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

h_Slant = sqrt(h^2+(3*V)/(pi*h)) --> sqrt(5^2+(3*520)/(pi*5))

Evaluating ... ...

h_Slant = 11.1495598338833

STEP 3: Convert Result to Output's Unit

11.1495598338833 Meter --> No Conversion Required

FINAL ANSWER

11.1495598338833 ≈ 11.14956 Meter <-- Slant Height of Cone

(Calculation completed in 00.004 seconds)

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

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< Slant Height of Cone Calculators

Slant Height of Cone given Volume

LaTeX 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 Total Surface Area

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

Slant Height of Cone given Lateral Surface Area

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

Slant Height of Cone

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

Slant Height of Cone given Volume and Height Formula

LaTeX Go

Slant Height of Cone = sqrt(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone))
h_Slant = sqrt(h^2+(3*V)/(pi*h))

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 Height?

Slant Height of Cone given Volume and Height calculator uses Slant Height of Cone = sqrt(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone)) to calculate the Slant Height of Cone, The Slant Height of Cone given Volume and Height 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 height of the Cone. Slant Height of Cone is denoted by h_Slant symbol.

How to calculate Slant Height of Cone given Volume and Height using this online calculator? To use this online calculator for Slant Height of Cone given Volume and Height, enter Height of Cone (h) & Volume of Cone (V) and hit the calculate button. Here is how the Slant Height of Cone given Volume and Height calculation can be explained with given input values -> 11.14956 = sqrt(5^2+(3*520)/(pi*5)).

FAQ

What is Slant Height of Cone given Volume and Height?

The Slant Height of Cone given Volume and Height 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 height of the Cone and is represented as h_Slant = sqrt(h^2+(3*V)/(pi*h)) or Slant Height of Cone = sqrt(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone)). Height of Cone is defined as the distance between the apex of the Cone to the center of its circular base & Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone.

How to calculate Slant Height of Cone given Volume and Height?

The Slant Height of Cone given Volume and Height 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 height of the Cone is calculated using Slant Height of Cone = sqrt(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone)). To calculate Slant Height of Cone given Volume and Height, you need Height of Cone (h) & Volume of Cone (V). With our tool, you need to enter the respective value for Height 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 Slant Height of Cone?

In this formula, Slant Height of Cone uses Height of Cone & Volume of Cone. We can use 3 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)

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