Volume of Truncated Cone given Total Surface Area 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%
✖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 [TSA]			+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 given Total Surface Area [V]

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Volume of Truncated Cone given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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.

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
Total Surface Area of Truncated Cone: 260 Square Meter --> 260 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = pi/3*(r_Base^2+(r_Base*r_Top)+r_Top^2)*sqrt(((TSA-pi*(r_Base^2+r_Top^2))/(pi*(r_Base+r_Top)))^2-(r_Base-r_Top)^2) --> pi/3*(5^2+(5*2)+2^2)*sqrt(((260-pi*(5^2+2^2))/(pi*(5+2)))^2-(5-2)^2)

Evaluating ... ...

V = 288.740175130563

STEP 3: Convert Result to Output's Unit

288.740175130563 Cubic Meter --> No Conversion Required

FINAL ANSWER

288.740175130563 ≈ 288.7402 Cubic Meter <-- Volume of Truncated Cone

(Calculation completed in 00.020 seconds)

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

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Created by Nikhil

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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< Volume of Truncated Cone Calculators

Volume of Truncated Cone given Total Surface Area

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

Volume of Truncated Cone given Curved Surface Area

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

Volume of Truncated Cone given Slant Height

LaTeX Go Volume of Truncated Cone = pi/3*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2)*sqrt(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2)

Volume of Truncated Cone

LaTeX Go Volume of Truncated Cone = pi/3*Height of Truncated Cone*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2)

Volume of Truncated Cone given Total Surface Area Formula

LaTeX Go

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 Volume of Truncated Cone given Total Surface Area?

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

How to calculate Volume of Truncated Cone given Total Surface Area using this online calculator? To use this online calculator for Volume of Truncated Cone given Total Surface Area, enter Base Radius of Truncated Cone (r_Base), Top Radius of Truncated Cone (r_Top) & Total Surface Area of Truncated Cone (TSA) and hit the calculate button. Here is how the Volume of Truncated Cone given Total Surface Area calculation can be explained with given input values -> 288.7402 = pi/3*(5^2+(5*2)+2^2)*sqrt(((260-pi*(5^2+2^2))/(pi*(5+2)))^2-(5-2)^2).

FAQ

What is Volume of Truncated Cone given Total Surface Area?

Volume of Truncated Cone given Total Surface Area formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone, and calculated using the total surface area of Truncated Cone and is represented as V = pi/3*(r_Base^2+(r_Base*r_Top)+r_Top^2)*sqrt(((TSA-pi*(r_Base^2+r_Top^2))/(pi*(r_Base+r_Top)))^2-(r_Base-r_Top)^2) or Volume of Truncated Cone = pi/3*(Base Radius of Truncated Cone^2+(Base Radius of Truncated Cone*Top Radius of Truncated Cone)+Top Radius of Truncated Cone^2)*sqrt(((Total Surface Area of Truncated Cone-pi*(Base Radius of Truncated Cone^2+Top Radius of Truncated Cone^2))/(pi*(Base Radius of Truncated Cone+Top Radius of Truncated Cone)))^2-(Base Radius of Truncated Cone-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 & Total Surface Area of Truncated Cone is the quantity of plane enclosed by the entire surface of the Truncated Cone.

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

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

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

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

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