Volume of Cone given Slant Height 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%
✖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 [h_Slant]			+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 Slant Height [V]

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Formula

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Volume of Cone given Slant Height

Formula

`"V" = (pi*"r"_{"Base"}^2*sqrt("h"_{"Slant"}^2-"r"_{"Base"}^2))/3`

Example

`"479.8862m³"=(pi*("10m")^2*sqrt(("11m")^2-("10m")^2))/3`

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Volume of Cone given Slant Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Cone = (pi*Base Radius of Cone^2*sqrt(Slant Height of Cone^2-Base Radius of Cone^2))/3
V = (pi*r_Base^2*sqrt(h_Slant^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.
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.

STEP 1: Convert Input(s) to Base Unit

Base Radius of Cone: 10 Meter --> 10 Meter No Conversion Required
Slant Height of Cone: 11 Meter --> 11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (pi*r_Base^2*sqrt(h_Slant^2-r_Base^2))/3 --> (pi*10^2*sqrt(11^2-10^2))/3

Evaluating ... ...

V = 479.88620459308

STEP 3: Convert Result to Output's Unit

479.88620459308 Cubic Meter --> No Conversion Required

FINAL ANSWER

479.88620459308 ≈ 479.8862 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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The National Institute of Engineering (NIE), Mysuru

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< 13 Volume of Cone Calculators

Volume of Cone given Total Surface Area and Base Circumference

Go Volume of Cone = (pi*(Base Circumference of Cone/(2*pi))^2*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))/3

Volume of Cone given Total Surface Area and Base Area

Go Volume of Cone = (Base Area 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))/3

Volume of Cone given Lateral Surface Area and Base Circumference

Go Volume of Cone = (pi*(Base Circumference of Cone/(2*pi))^2*sqrt(((2*Lateral Surface Area of Cone)/Base Circumference of Cone)^2-(Base Circumference of Cone/(2*pi))^2))/3

Volume of Cone given Total Surface Area

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 Lateral Surface Area

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

Volume of Cone given Lateral Surface Area and Base Area

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

Volume of Cone given Slant Height and Base Circumference

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

Volume of Cone given Slant Height

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

Volume of Cone given Slant Height and Base Area

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

Volume of Cone given Slant Height and Height

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

Volume of Cone given Base Circumference

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

Volume of Cone

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

Volume of Cone given Base Area

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

Volume of Cone given Slant Height Formula

Volume of Cone = (pi*Base Radius of Cone^2*sqrt(Slant Height of Cone^2-Base Radius of Cone^2))/3
V = (pi*r_Base^2*sqrt(h_Slant^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 Slant Height?

Volume of Cone given Slant Height calculator uses Volume of Cone = (pi*Base Radius of Cone^2*sqrt(Slant Height of Cone^2-Base Radius of Cone^2))/3 to calculate the Volume of Cone, The Volume of Cone given Slant Height formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Cone, and calculated using the slant height of the Cone. Volume of Cone is denoted by V symbol.

How to calculate Volume of Cone given Slant Height using this online calculator? To use this online calculator for Volume of Cone given Slant Height, enter Base Radius of Cone (r_Base) & Slant Height of Cone (h_Slant) and hit the calculate button. Here is how the Volume of Cone given Slant Height calculation can be explained with given input values -> 479.8862 = (pi*10^2*sqrt(11^2-10^2))/3.

FAQ

What is Volume of Cone given Slant Height?

The Volume of Cone given Slant Height formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Cone, and calculated using the slant height of the Cone and is represented as V = (pi*r_Base^2*sqrt(h_Slant^2-r_Base^2))/3 or Volume of Cone = (pi*Base Radius of Cone^2*sqrt(Slant Height 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 & 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.

How to calculate Volume of Cone given Slant Height?

The Volume of Cone given Slant Height formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Cone, and calculated using the slant height of the Cone is calculated using Volume of Cone = (pi*Base Radius of Cone^2*sqrt(Slant Height of Cone^2-Base Radius of Cone^2))/3. To calculate Volume of Cone given Slant Height, you need Base Radius of Cone (r_Base) & Slant Height of Cone (h_Slant). With our tool, you need to enter the respective value for Base Radius of Cone & Slant Height 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 & Slant Height of Cone. We can use 12 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)
Volume of Cone = (pi*(Slant Height of Cone^2-Height of Cone^2)*Height of Cone)/3
Volume of Cone = (Base Area of Cone*sqrt(Slant Height of Cone^2-Base Area of Cone/pi))/3
Volume of Cone = (Base Circumference of Cone^2*sqrt(Slant Height of Cone^2-(Base Circumference of Cone/(2*pi))^2))/(12*pi)
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 = (Base Area 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))/3
Volume of Cone = (pi*(Base Circumference of Cone/(2*pi))^2*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))/3
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
Volume of Cone = (Base Area of Cone*sqrt(Lateral Surface Area of Cone^2/(pi*Base Area of Cone)-Base Area of Cone/pi))/3
Volume of Cone = (pi*(Base Circumference of Cone/(2*pi))^2*sqrt(((2*Lateral Surface Area of Cone)/Base Circumference of Cone)^2-(Base Circumference of Cone/(2*pi))^2))/3

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