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

✖Base Area of Cone is the total quantity of plane enclosed on the base circular surface of the Cone.ⓘ Base Area of Cone [A_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%

✖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 given Slant Height and Base Area [TSA]

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Total Surface Area of Cone given Slant Height and Base Area

Formula

`"TSA" = (sqrt(pi*"A"_{"Base"})*"h"_{"Slant"})+"A"_{"Base"}`

Example

`"661.0373m²"=(sqrt(pi*"315m²")*"11m")+"315m²"`

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

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Cone = (sqrt(pi*Base Area of Cone)*Slant Height of Cone)+Base Area of Cone
TSA = (sqrt(pi*A_Base)*h_Slant)+A_Base
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

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.
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.
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 Area of Cone: 315 Square Meter --> 315 Square Meter No Conversion Required
Slant Height of Cone: 11 Meter --> 11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (sqrt(pi*A_Base)*h_Slant)+A_Base --> (sqrt(pi*315)*11)+315

Evaluating ... ...

TSA = 661.037286996033

STEP 3: Convert Result to Output's Unit

661.037286996033 Square Meter --> No Conversion Required

FINAL ANSWER

661.037286996033 ≈ 661.0373 Square Meter <-- Total Surface Area of Cone

(Calculation completed in 00.020 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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< 14 Total Surface Area of Cone Calculators

Total Surface Area of Cone given Volume and Height

Go Total Surface Area of Cone = (3*Volume of Cone)/Height of Cone+pi*sqrt((3*Volume of Cone)/(pi*Height of Cone)*(Height of Cone^2+(3*Volume of Cone)/(pi*Height of Cone)))

Total Surface Area of Cone given Volume and Base Circumference

Go Total Surface Area of Cone = (Base Circumference of Cone^2)/(4*pi)+Base Circumference of Cone/2*sqrt(((3*Volume of Cone)/(Base Circumference of Cone^2/(4*pi)))^2+(Base Circumference of Cone/(2*pi))^2)

Total Surface Area of Cone given Volume

Go Total Surface Area of Cone = (3*Volume of Cone)/Height of Cone+pi*Base Radius of Cone*sqrt(((3*Volume of Cone)/(pi*Base Radius of Cone^2))^2+Base Radius of Cone^2)

Total Surface Area of Cone given Volume and Base Area

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

Total Surface Area of Cone given Height and Base Circumference

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

Total Surface Area of Cone given Height and Base Area

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

Total Surface Area of Cone given Height

Go Total Surface Area of Cone = pi*Base Radius of Cone^2+pi*Base Radius of Cone*sqrt(Height of Cone^2+Base Radius of Cone^2)

Total Surface Area of Cone given Slant Height and Base Area

Go Total Surface Area of Cone = (sqrt(pi*Base Area of Cone)*Slant Height of Cone)+Base Area of Cone

Total Surface Area of Cone given Slant Height and Base Circumference

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

Total Surface Area of Cone

Go Total Surface Area of Cone = pi*Base Radius of Cone*(Base Radius of Cone+Slant Height of Cone)

Total Surface Area of Cone given Base Area

Go Total Surface Area of Cone = (pi*Base Radius of Cone*Slant Height of Cone)+Base Area of Cone

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

Go Total Surface Area of Cone = Lateral Surface Area of Cone+Base Circumference of Cone^2/(4*pi)

Total Surface Area of Cone given Lateral Surface Area

Go Total Surface Area of Cone = Lateral Surface Area of Cone+(pi*Base Radius of Cone^2)

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

Go Total Surface Area of Cone = Lateral Surface Area of Cone+Base Area of Cone

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

Total Surface Area of Cone = (sqrt(pi*Base Area of Cone)*Slant Height of Cone)+Base Area of Cone
TSA = (sqrt(pi*A_Base)*h_Slant)+A_Base

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

Total Surface Area of Cone given Slant Height and Base Area calculator uses Total Surface Area of Cone = (sqrt(pi*Base Area of Cone)*Slant Height of Cone)+Base Area of Cone to calculate the Total Surface Area of Cone, The Total Surface Area of Cone given Slant Height and Base Area formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the slant height and base area of the Cone. Total Surface Area of Cone is denoted by TSA symbol.

How to calculate Total Surface Area of Cone given Slant Height and Base Area using this online calculator? To use this online calculator for Total Surface Area of Cone given Slant Height and Base Area, enter Base Area of Cone (A_Base) & Slant Height of Cone (h_Slant) and hit the calculate button. Here is how the Total Surface Area of Cone given Slant Height and Base Area calculation can be explained with given input values -> 661.0373 = (sqrt(pi*315)*11)+315.

FAQ

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

The Total Surface Area of Cone given Slant Height and Base Area formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the slant height and base area of the Cone and is represented as TSA = (sqrt(pi*A_Base)*h_Slant)+A_Base or Total Surface Area of Cone = (sqrt(pi*Base Area of Cone)*Slant Height of Cone)+Base Area of Cone. Base Area of Cone is the total quantity of plane enclosed on 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 Total Surface Area of Cone given Slant Height and Base Area?

The Total Surface Area of Cone given Slant Height and Base Area formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the slant height and base area of the Cone is calculated using Total Surface Area of Cone = (sqrt(pi*Base Area of Cone)*Slant Height of Cone)+Base Area of Cone. To calculate Total Surface Area of Cone given Slant Height and Base Area, you need Base Area of Cone (A_Base) & Slant Height of Cone (h_Slant). With our tool, you need to enter the respective value for Base Area 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 Total Surface Area of Cone?

In this formula, Total Surface Area of Cone uses Base Area of Cone & Slant Height of Cone. We can use 13 other way(s) to calculate the same, which is/are as follows -

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

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