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

STEP 0: Pre-Calculation Summary
Formula Used
Base Area of Cone = pi/4*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone)^2
ABase = pi/4*(sqrt(hSlant^2+(4*TSA)/pi)-hSlant)^2
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 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.
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
ABase = pi/4*(sqrt(hSlant^2+(4*TSA)/pi)-hSlant)^2 --> pi/4*(sqrt(11^2+(4*665)/pi)-11)^2
Evaluating ... ...
ABase = 317.559637090971
STEP 3: Convert Result to Output's Unit
317.559637090971 Square Meter --> No Conversion Required
FINAL ANSWER
317.559637090971 317.5596 Square Meter <-- Base Area 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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7 Base Area of Cone Calculators

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

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

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

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 Area of Cone given Total Surface Area and Slant Height?

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

How to calculate Base Area of Cone given Total Surface Area and Slant Height using this online calculator? To use this online calculator for Base Area of Cone given Total Surface Area and Slant Height, enter Slant Height of Cone (hSlant) & Total Surface Area of Cone (TSA) and hit the calculate button. Here is how the Base Area of Cone given Total Surface Area and Slant Height calculation can be explained with given input values -> 317.5596 = pi/4*(sqrt(11^2+(4*665)/pi)-11)^2.

FAQ

What is Base Area of Cone given Total Surface Area and Slant Height?
The Base Area of Cone given Total Surface Area and Slant Height formula is defined as the total quantity of plane enclosed on the base circular surface of the Cone, and calculated using the total surface area and slant height of the Cone and is represented as ABase = pi/4*(sqrt(hSlant^2+(4*TSA)/pi)-hSlant)^2 or Base Area of Cone = pi/4*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone)^2. 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 Area of Cone given Total Surface Area and Slant Height?
The Base Area of Cone given Total Surface Area and Slant Height formula is defined as the total quantity of plane enclosed on the base circular surface of the Cone, and calculated using the total surface area and slant height of the Cone is calculated using Base Area of Cone = pi/4*(sqrt(Slant Height of Cone^2+(4*Total Surface Area of Cone)/pi)-Slant Height of Cone)^2. To calculate Base Area of Cone given Total Surface Area and Slant Height, you need Slant Height of Cone (hSlant) & 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 Area of Cone?
In this formula, Base Area 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 Area of Cone = pi*Base Radius of Cone^2
  • Base Area of Cone = (Base Circumference of Cone^2)/(4*pi)
  • Base Area of Cone = pi*(Lateral Surface Area of Cone/(pi*Slant Height of Cone))^2
  • Base Area of Cone = pi*(Slant Height of Cone^2-Height of Cone^2)
  • Base Area of Cone = (3*Volume of Cone)/Height of Cone
  • Base Area of Cone = Total Surface Area of Cone-Lateral Surface Area of Cone
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