Base Circumference of Cone given Total Surface Area and Slant Height Calculator

✖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%
✖Total Surface Area of Cone is defined as the total quantity of plane enclosed on the entire surface of the Cone.ⓘ Total Surface Area of Cone [TSA]			+10% -10%

✖Base Circumference of Cone is the total length of the boundary of the base circular surface of the Cone.ⓘ Base Circumference of Cone given Total Surface Area and Slant Height [C_Base]

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Formula

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Base Circumference of Cone given Total Surface Area and Slant Height

Formula

`"C"_{"Base"} = pi*(sqrt("h"_{"Slant"}^2+(4*"TSA")/pi)-"h"_{"Slant"})`

Example

`"63.17098m"=pi*(sqrt(("11m")^2+(4*"665m²")/pi)-"11m")`

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Base Circumference of Cone given Total Surface Area and Slant Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Base Circumference of Cone = pi*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone)
C_Base = pi*(sqrt(h_Slant^2+(4*TSA)/pi)-h_Slant)
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

Base Circumference of Cone - (Measured in Meter) - Base Circumference of Cone is the total length of the boundary 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.
Total Surface Area of Cone - (Measured in Square Meter) - Total Surface Area of Cone is defined as the total quantity of plane enclosed on the entire surface of the Cone.

STEP 1: Convert Input(s) to Base Unit

Slant Height of Cone: 11 Meter --> 11 Meter No Conversion Required
Total Surface Area of Cone: 665 Square Meter --> 665 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_Base = pi*(sqrt(h_Slant^2+(4*TSA)/pi)-h_Slant) --> pi*(sqrt(11^2+(4*665)/pi)-11)

Evaluating ... ...

C_Base = 63.1709750743689

STEP 3: Convert Result to Output's Unit

63.1709750743689 Meter --> No Conversion Required

FINAL ANSWER

63.1709750743689 ≈ 63.17098 Meter <-- Base Circumference 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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< 7 Base Circumference of Cone Calculators

Base Circumference of Cone given Total Surface Area and Slant Height

Go Base Circumference of Cone = pi*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone)

Base Circumference of Cone given Total Surface Area and Lateral Surface Area

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

Base Circumference of Cone given Volume

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

Base Circumference of Cone given Slant Height

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

Base Circumference of Cone given Base Area

Go Base Circumference of Cone = 2*sqrt(pi*Base Area of Cone)

Base Circumference of Cone given Lateral Surface Area and Slant Height

Go Base Circumference of Cone = 2*Lateral Surface Area of Cone/Slant Height of Cone

Base Circumference of Cone

Go Base Circumference of Cone = 2*pi*Base Radius of Cone

Base Circumference of Cone given Total Surface Area and Slant Height Formula

Base Circumference of Cone = pi*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone)
C_Base = pi*(sqrt(h_Slant^2+(4*TSA)/pi)-h_Slant)

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 Base Circumference of Cone given Total Surface Area and Slant Height?

Base Circumference of Cone given Total Surface Area and Slant Height calculator uses Base Circumference of Cone = pi*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone) to calculate the Base Circumference of Cone, The Base Circumference of Cone given Total Surface Area and Slant Height formula is defined as the total length of the boundary of the base circular surface of the Cone, and calculated using the total surface area and slant height of the Cone. Base Circumference of Cone is denoted by C_Base symbol.

How to calculate Base Circumference of Cone given Total Surface Area and Slant Height using this online calculator? To use this online calculator for Base Circumference of Cone given Total Surface Area and Slant Height, enter Slant Height of Cone (h_Slant) & Total Surface Area of Cone (TSA) and hit the calculate button. Here is how the Base Circumference of Cone given Total Surface Area and Slant Height calculation can be explained with given input values -> 63.17098 = pi*(sqrt(11^2+(4*665)/pi)-11).

FAQ

What is Base Circumference of Cone given Total Surface Area and Slant Height?

The Base Circumference of Cone given Total Surface Area and Slant Height formula is defined as the total length of the boundary of the base circular surface of the Cone, and calculated using the total surface area and slant height of the Cone and is represented as C_Base = pi*(sqrt(h_Slant^2+(4*TSA)/pi)-h_Slant) or Base Circumference of Cone = pi*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of 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 & Total Surface Area of Cone is defined as the total quantity of plane enclosed on the entire surface of the Cone.

How to calculate Base Circumference of Cone given Total Surface Area and Slant Height?

The Base Circumference of Cone given Total Surface Area and Slant Height formula is defined as the total length of the boundary of the base circular surface of the Cone, and calculated using the total surface area and slant height of the Cone is calculated using Base Circumference of Cone = pi*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone). To calculate Base Circumference of Cone given Total Surface Area and Slant Height, you need Slant Height of Cone (h_Slant) & Total Surface Area of Cone (TSA). With our tool, you need to enter the respective value for Slant Height of Cone & Total Surface 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 Base Circumference of Cone?

In this formula, Base Circumference of Cone uses Slant Height of Cone & Total Surface Area of Cone. We can use 6 other way(s) to calculate the same, which is/are as follows -

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

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