Total Surface Area of Cone given Volume and Base Circumference Calculator

✖Base Circumference of Cone is the total length of the boundary of the base circular surface of the Cone.ⓘ Base Circumference of Cone [C_Base]			+10% -10%
✖Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone.ⓘ Volume of Cone [V]			+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 Volume and Base Circumference [TSA]

⎘ Copy

👎

Formula

✖

Total Surface Area of Cone given Volume and Base Circumference

Formula

`"TSA" = ("C"_{"Base"}^2)/(4*pi)+"C"_{"Base"}/2*sqrt(((3*"V")/("C"_{"Base"}^2/(4*pi)))^2+("C"_{"Base"}/(2*pi))^2)`

Example

`"616.263m²"=(("60m")^2)/(4*pi)+"60m"/2*sqrt(((3*"520m³")/(("60m")^2/(4*pi)))^2+("60m"/(2*pi))^2)`

Calculator

LaTeX

Reset

👍

Download Cone Formula PDF PDF Image

Total Surface Area of Cone given Volume and Base Circumference Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
TSA = (C_Base^2)/(4*pi)+C_Base/2*sqrt(((3*V)/(C_Base^2/(4*pi)))^2+(C_Base/(2*pi))^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 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.
Volume of Cone - (Measured in Cubic Meter) - Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone.

STEP 1: Convert Input(s) to Base Unit

Base Circumference of Cone: 60 Meter --> 60 Meter No Conversion Required
Volume of Cone: 520 Cubic Meter --> 520 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (C_Base^2)/(4*pi)+C_Base/2*sqrt(((3*V)/(C_Base^2/(4*pi)))^2+(C_Base/(2*pi))^2) --> (60^2)/(4*pi)+60/2*sqrt(((3*520)/(60^2/(4*pi)))^2+(60/(2*pi))^2)

Evaluating ... ...

TSA = 616.263022487821

STEP 3: Convert Result to Output's Unit

616.263022487821 Square Meter --> No Conversion Required

FINAL ANSWER

616.263022487821 ≈ 616.263 Square Meter <-- Total Surface Area of Cone

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Cone » Cone » Surface Area of Cone » Total Surface Area of Cone » Total Surface Area of Cone given Volume and Base Circumference

Credits

Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has created this Calculator and 1100+ more calculators!

Verified by Nikita Kumari

The National Institute of Engineering (NIE), Mysuru

Nikita Kumari has verified this Calculator and 600+ more calculators!

< 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 Volume and Base Circumference Formula

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 Volume and Base Circumference?

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

How to calculate Total Surface Area of Cone given Volume and Base Circumference using this online calculator? To use this online calculator for Total Surface Area of Cone given Volume and Base Circumference, enter Base Circumference of Cone (C_Base) & Volume of Cone (V) and hit the calculate button. Here is how the Total Surface Area of Cone given Volume and Base Circumference calculation can be explained with given input values -> 616.263 = (60^2)/(4*pi)+60/2*sqrt(((3*520)/(60^2/(4*pi)))^2+(60/(2*pi))^2).

FAQ

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

The Total Surface Area of Cone given Volume and Base Circumference formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the volume and base circumference of the Cone and is represented as TSA = (C_Base^2)/(4*pi)+C_Base/2*sqrt(((3*V)/(C_Base^2/(4*pi)))^2+(C_Base/(2*pi))^2) or 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). Base Circumference of Cone is the total length of the boundary of the base circular surface of the Cone & Volume of Cone is defined as the total quantity of three-dimensional space enclosed by the entire surface of the Cone.

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

The Total Surface Area of Cone given Volume and Base Circumference formula is defined as the total quantity of plane enclosed on the entire surface of the Cone, and calculated using the volume and base circumference of the Cone is calculated using 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). To calculate Total Surface Area of Cone given Volume and Base Circumference, you need Base Circumference of Cone (C_Base) & Volume of Cone (V). With our tool, you need to enter the respective value for Base Circumference of Cone & Volume 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 Circumference of Cone & Volume 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 = (sqrt(pi*Base Area of Cone)*Slant Height 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(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)

Home

FREE PDFs

🔍 Search