Total Surface Area of Truncated Cone given Volume Calculator

✖Base Radius of Truncated Cone is the distance between the center and any point on the circumference of the base circular surface of the Truncated Cone.ⓘ Base Radius of Truncated Cone [r_Base]			+10% -10%
✖Top Radius of Truncated Cone is the distance between the center and any point on the circumference of the top circular surface of the Truncated Cone.ⓘ Top Radius of Truncated Cone [r_Top]			+10% -10%
✖Volume of Truncated Cone is the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone.ⓘ Volume of Truncated Cone [V]			+10% -10%

✖Total Surface Area of Truncated Cone is the quantity of plane enclosed by the entire surface of the Truncated Cone.ⓘ Total Surface Area of Truncated Cone given Volume [TSA]

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Formula

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Total Surface Area of Truncated Cone given Volume

Formula

`"TSA" = (pi*("r"_{"Base"}+"r"_{"Top"})*sqrt(((3*"V")/(pi*("r"_{"Base"}^2+("r"_{"Base"}*"r"_{"Top"})+"r"_{"Top"}^2)))^2+("r"_{"Base"}-"r"_{"Top"})^2))+(pi*("r"_{"Base"}^2+"r"_{"Top"}^2))`

Example

`"260.6247m²"=(pi*("5m"+"2m")*sqrt(((3*"290m³")/(pi*(("5m")^2+("5m"*"2m")+("2m")^2)))^2+("5m"-"2m")^2))+(pi*(("5m")^2+("2m")^2))`

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Total Surface Area of Truncated Cone given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Truncated Cone = (pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)*sqrt(((3*Volume of Truncated Cone)/(pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2)))^2+(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2))+(pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))
TSA = (pi*(r_Base+r_Top)*sqrt(((3*V)/(pi*(r_Base^2+(r_Base*r_Top)+r_Top^2)))^2+(r_Base-r_Top)^2))+(pi*(r_Base^2+r_Top^2))
This formula uses 1 Constants, 1 Functions, 4 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 Truncated Cone - (Measured in Square Meter) - Total Surface Area of Truncated Cone is the quantity of plane enclosed by the entire surface of the Truncated Cone.
Base Radius of Truncated Cone - (Measured in Meter) - Base Radius of Truncated Cone is the distance between the center and any point on the circumference of the base circular surface of the Truncated Cone.
Top Radius of Truncated Cone - (Measured in Meter) - Top Radius of Truncated Cone is the distance between the center and any point on the circumference of the top circular surface of the Truncated Cone.
Volume of Truncated Cone - (Measured in Cubic Meter) - Volume of Truncated Cone is the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone.

STEP 1: Convert Input(s) to Base Unit

Base Radius of Truncated Cone: 5 Meter --> 5 Meter No Conversion Required
Top Radius of Truncated Cone: 2 Meter --> 2 Meter No Conversion Required
Volume of Truncated Cone: 290 Cubic Meter --> 290 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = (pi*(r_Base+r_Top)*sqrt(((3*V)/(pi*(r_Base^2+(r_Base*r_Top)+r_Top^2)))^2+(r_Base-r_Top)^2))+(pi*(r_Base^2+r_Top^2)) --> (pi*(5+2)*sqrt(((3*290)/(pi*(5^2+(5*2)+2^2)))^2+(5-2)^2))+(pi*(5^2+2^2))

Evaluating ... ...

TSA = 260.624679188785

STEP 3: Convert Result to Output's Unit

260.624679188785 Square Meter --> No Conversion Required

FINAL ANSWER

260.624679188785 ≈ 260.6247 Square Meter <-- Total Surface Area of Truncated Cone

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Cone » Truncated Cone » Surface Area of Truncated Cone » Total Surface Area of Truncated Cone » Total Surface Area of Truncated Cone given Volume

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Mumbai University (DJSCE), Mumbai

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

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< 4 Total Surface Area of Truncated Cone Calculators

Total Surface Area of Truncated Cone given Volume

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

Total Surface Area of Truncated Cone

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

Total Surface Area of Truncated Cone given Slant Height

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

Total Surface Area of Truncated Cone given Curved Surface Area

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

Total Surface Area of Truncated Cone given Volume Formula

What is a Truncated Cone?

A Truncated Cone is basically a circular cone of which top is cut or 'truncated' by a horizontal plane. Or in another way, a Truncated Cone is formed when a smaller circular cone is cut from the top of a larger circular cone. The Truncated has two circular surfaces - one on top and another on the bottom, and a lateral curved surface. The slant height is the shortest distance between the two circles on the lateral surface, which is the surface without the circles.

How to Calculate Total Surface Area of Truncated Cone given Volume?

Total Surface Area of Truncated Cone given Volume calculator uses Total Surface Area of Truncated Cone = (pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)*sqrt(((3*Volume of Truncated Cone)/(pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2)))^2+(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2))+(pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2)) to calculate the Total Surface Area of Truncated Cone, The Total Surface Area of Truncated Cone given Volume formula is defined as the quantity of plane enclosed by the entire surface of the Truncated Cone, and calculated using the volume of Truncated Cone. Total Surface Area of Truncated Cone is denoted by TSA symbol.

How to calculate Total Surface Area of Truncated Cone given Volume using this online calculator? To use this online calculator for Total Surface Area of Truncated Cone given Volume, enter Base Radius of Truncated Cone (r_Base), Top Radius of Truncated Cone (r_Top) & Volume of Truncated Cone (V) and hit the calculate button. Here is how the Total Surface Area of Truncated Cone given Volume calculation can be explained with given input values -> 260.6247 = (pi*(5+2)*sqrt(((3*290)/(pi*(5^2+(5*2)+2^2)))^2+(5-2)^2))+(pi*(5^2+2^2)).

FAQ

What is Total Surface Area of Truncated Cone given Volume?

The Total Surface Area of Truncated Cone given Volume formula is defined as the quantity of plane enclosed by the entire surface of the Truncated Cone, and calculated using the volume of Truncated Cone and is represented as TSA = (pi*(r_Base+r_Top)*sqrt(((3*V)/(pi*(r_Base^2+(r_Base*r_Top)+r_Top^2)))^2+(r_Base-r_Top)^2))+(pi*(r_Base^2+r_Top^2)) or Total Surface Area of Truncated Cone = (pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)*sqrt(((3*Volume of Truncated Cone)/(pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2)))^2+(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2))+(pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2)). Base Radius of Truncated Cone is the distance between the center and any point on the circumference of the base circular surface of the Truncated Cone, Top Radius of Truncated Cone is the distance between the center and any point on the circumference of the top circular surface of the Truncated Cone & Volume of Truncated Cone is the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone.

How to calculate Total Surface Area of Truncated Cone given Volume?

The Total Surface Area of Truncated Cone given Volume formula is defined as the quantity of plane enclosed by the entire surface of the Truncated Cone, and calculated using the volume of Truncated Cone is calculated using Total Surface Area of Truncated Cone = (pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)*sqrt(((3*Volume of Truncated Cone)/(pi*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2)))^2+(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2))+(pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2)). To calculate Total Surface Area of Truncated Cone given Volume, you need Base Radius of Truncated Cone (r_Base), Top Radius of Truncated Cone (r_Top) & Volume of Truncated Cone (V). With our tool, you need to enter the respective value for Base Radius of Truncated Cone, Top Radius of Truncated Cone & Volume of Truncated 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 Truncated Cone?

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

Total Surface Area of Truncated Cone = Curved Surface Area of Truncated Cone+pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2)
Total Surface Area of Truncated Cone = pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2+(sqrt((Top Radius of Truncated Cone-Base Radius of Truncated Cone)^2+Height of Truncated Cone^2)*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))
Total Surface Area of Truncated Cone = pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2+(Slant Height of Truncated Cone*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))

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