Total Surface Area of Cone given 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%
✖Height of Cone is defined as the distance between the apex of the Cone to the center of its circular base.ⓘ Height of Cone [h]			+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 Height [TSA]

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Total Surface Area of Cone given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
TSA = pi*r_Base^2+pi*r_Base*sqrt(h^2+r_Base^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

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 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.
Height of Cone - (Measured in Meter) - Height of Cone is defined as the distance between the apex of the Cone to the center of its circular base.

STEP 1: Convert Input(s) to Base Unit

Base Radius of Cone: 10 Meter --> 10 Meter No Conversion Required
Height of Cone: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = pi*r_Base^2+pi*r_Base*sqrt(h^2+r_Base^2) --> pi*10^2+pi*10*sqrt(5^2+10^2)

Evaluating ... ...

TSA = 665.400001911016

STEP 3: Convert Result to Output's Unit

665.400001911016 Square Meter --> No Conversion Required

FINAL ANSWER

665.400001911016 ≈ 665.4 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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< Total Surface Area of Cone Calculators

Total Surface Area of Cone

LaTeX 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

LaTeX 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

LaTeX 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

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

Total Surface Area of Cone given Height Formula

LaTeX 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)
TSA = pi*r_Base^2+pi*r_Base*sqrt(h^2+r_Base^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 Total Surface Area of Cone given Height?

Total Surface Area of Cone given Height calculator uses 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) to calculate the Total Surface Area of Cone, The Total Surface Area of Cone given Height formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the height of the Cone. Total Surface Area of Cone is denoted by TSA symbol.

How to calculate Total Surface Area of Cone given Height using this online calculator? To use this online calculator for Total Surface Area of Cone given Height, enter Base Radius of Cone (r_Base) & Height of Cone (h) and hit the calculate button. Here is how the Total Surface Area of Cone given Height calculation can be explained with given input values -> 665.4 = pi*10^2+pi*10*sqrt(5^2+10^2).

FAQ

What is Total Surface Area of Cone given Height?

The Total Surface Area of Cone given Height formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the height of the Cone and is represented as TSA = pi*r_Base^2+pi*r_Base*sqrt(h^2+r_Base^2) or 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). 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 & Height of Cone is defined as the distance between the apex of the Cone to the center of its circular base.

How to calculate Total Surface Area of Cone given Height?

The Total Surface Area of Cone given Height formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the height of the Cone is calculated using 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). To calculate Total Surface Area of Cone given Height, you need Base Radius of Cone (r_Base) & Height of Cone (h). With our tool, you need to enter the respective value for Base Radius of Cone & 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 Radius of Cone & Height of Cone. We can use 3 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

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