Base Radius 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 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 given Total Surface Area and Slant Height [r_Base]

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

STEP 0: Pre-Calculation Summary

Formula Used

Base Radius of Cone = 1/2*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone)
r_Base = 1/2*(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 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.
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

r_Base = 1/2*(sqrt(h_Slant^2+(4*TSA)/pi)-h_Slant) --> 1/2*(sqrt(11^2+(4*665)/pi)-11)

Evaluating ... ...

r_Base = 10.0539729430207

STEP 3: Convert Result to Output's Unit

10.0539729430207 Meter --> No Conversion Required

FINAL ANSWER

10.0539729430207 ≈ 10.05397 Meter <-- Base Radius of Cone

(Calculation completed in 00.020 seconds)

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< Base Radius of Cone Calculators

Base Radius of Cone given Total Surface Area and Slant Height

LaTeX Go Base Radius of Cone = 1/2*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone)

Base Radius of Cone given Volume

LaTeX Go Base Radius of Cone = sqrt((3*Volume of Cone)/(pi*Height of Cone))

Base Radius of Cone given Lateral Surface Area and Slant Height

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

Base Radius of Cone given Base Area

LaTeX Go Base Radius of Cone = sqrt(Base Area of Cone/pi)

< Base Radius of Cone Calculators

Base Radius of Cone given Total Surface Area and Slant Height

LaTeX Go Base Radius of Cone = 1/2*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone)

Base Radius of Cone given Volume

LaTeX Go Base Radius of Cone = sqrt((3*Volume of Cone)/(pi*Height of Cone))

Base Radius of Cone given Lateral Surface Area and Slant Height

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

Base Radius of Cone given Base Area

LaTeX Go Base Radius of Cone = sqrt(Base Area of Cone/pi)

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

LaTeX Go

Base Radius of Cone = 1/2*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone)
r_Base = 1/2*(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 Radius of Cone given Total Surface Area and Slant Height?

Base Radius of Cone given Total Surface Area and Slant Height calculator uses Base Radius of Cone = 1/2*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone) to calculate the Base Radius of Cone, Base Radius of Cone given Total Surface Area and Slant Height formula is defined as the distance between the center and any point on the circumference of the base circular surface of the Cone, and calculated using the total surface area and slant height of the Cone. Base Radius of Cone is denoted by r_Base symbol.

How to calculate Base Radius of Cone given Total Surface Area and Slant Height using this online calculator? To use this online calculator for Base Radius 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 Radius of Cone given Total Surface Area and Slant Height calculation can be explained with given input values -> 10.05397 = 1/2*(sqrt(11^2+(4*665)/pi)-11).

FAQ

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

Base Radius of Cone given Total Surface Area and Slant Height formula is defined as the distance between the center and any point on the circumference 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 r_Base = 1/2*(sqrt(h_Slant^2+(4*TSA)/pi)-h_Slant) or Base Radius of Cone = 1/2*(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 Radius of Cone given Total Surface Area and Slant Height?

Base Radius of Cone given Total Surface Area and Slant Height formula is defined as the distance between the center and any point on the circumference 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 Radius of Cone = 1/2*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone). To calculate Base Radius 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 Radius of Cone?

In this formula, Base Radius of Cone uses Slant Height of Cone & Total Surface Area of Cone. We can use 3 other way(s) to calculate the same, which is/are as follows -

Base Radius of Cone = sqrt(Base Area of Cone/pi)
Base Radius of Cone = Lateral Surface Area of Cone/(pi*Slant Height of Cone)
Base Radius of Cone = sqrt((3*Volume of Cone)/(pi*Height of Cone))

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