FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Volume of Truncated Cone given Total Surface Area Formula

GoVolume of Truncated Cone Formula

GoVolume of Truncated Cone given Curved Surface Area Formula

Fx Copy

LaTeX Copy

Volume of Truncated Cone is the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone. Check FAQs

V = \frac{π}{3} \cdot ({r Base}^{2} + (r Base \cdot r Top) + {r Top}^{2}) \cdot \sqrt{{(\frac{TSA - π \cdot ({r Base}^{2} + {r Top}^{2})}{π \cdot (r Base + r Top)})}^{2} - {(r Base - r Top)}^{2}}

V - Volume of Truncated Cone?r_Base - Base Radius of Truncated Cone?r_Top - Top Radius of Truncated Cone?TSA - Total Surface Area of Truncated Cone?π - Archimedes' constant?

Volume of Truncated Cone given Total Surface Area Example

With values

With units

Only example

Here is how the Volume of Truncated Cone given Total Surface Area equation looks like with Values.

Here is how the Volume of Truncated Cone given Total Surface Area equation looks like with Units.

Here is how the Volume of Truncated Cone given Total Surface Area equation looks like.

288.7402 = \frac{3.1416}{3} \cdot (5^{2} + (5 \cdot 2) + 2^{2}) \cdot \sqrt{{(\frac{260 - 3.1416 \cdot (5^{2} + 2^{2})}{3.1416 \cdot (5 + 2)})}^{2} - {(5 - 2)}^{2}}

288.7402m³ = \frac{3.1416}{3} \cdot ({5m}^{2} + (5m \cdot 2m) + {2m}^{2}) \cdot \sqrt{{(\frac{260m² - 3.1416 \cdot ({5m}^{2} + {2m}^{2})}{3.1416 \cdot (5m + 2m)})}^{2} - {(5m - 2m)}^{2}}

288.7402 = \frac{3.1416}{3} \cdot (5^{2} + (5 \cdot 2) + 2^{2}) \cdot \sqrt{{(\frac{260 - 3.1416 \cdot (5^{2} + 2^{2})}{3.1416 \cdot (5 + 2)})}^{2} - {(5 - 2)}^{2}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

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

Volume of Truncated Cone given Total Surface Area Solution

Follow our step by step solution on how to calculate Volume of Truncated Cone given Total Surface Area?

FIRST Step Consider the formula

V = \frac{π}{3} \cdot ({r Base}^{2} + (r Base \cdot r Top) + {r Top}^{2}) \cdot \sqrt{{(\frac{TSA - π \cdot ({r Base}^{2} + {r Top}^{2})}{π \cdot (r Base + r Top)})}^{2} - {(r Base - r Top)}^{2}}

Next Step Substitute values of Variables

∴

V = \frac{π}{3} \cdot ({5m}^{2} + (5m \cdot 2m) + {2m}^{2}) \cdot \sqrt{{(\frac{260m² - π \cdot ({5m}^{2} + {2m}^{2})}{π \cdot (5m + 2m)})}^{2} - {(5m - 2m)}^{2}}

Next Step Substitute values of Constants

∴

V = \frac{3.1416}{3} \cdot ({5m}^{2} + (5m \cdot 2m) + {2m}^{2}) \cdot \sqrt{{(\frac{260m² - 3.1416 \cdot ({5m}^{2} + {2m}^{2})}{3.1416 \cdot (5m + 2m)})}^{2} - {(5m - 2m)}^{2}}

Next Step Prepare to Evaluate

∴

V = \frac{3.1416}{3} \cdot (5^{2} + (5 \cdot 2) + 2^{2}) \cdot \sqrt{{(\frac{260 - 3.1416 \cdot (5^{2} + 2^{2})}{3.1416 \cdot (5 + 2)})}^{2} - {(5 - 2)}^{2}}

Next Step Evaluate

∴

V = 288.740175130563m³

LAST Step Rounding Answer

∴

V = 288.7402m³

Volume of Truncated Cone given Total Surface Area Formula Elements

Variables

Constants

Functions

Volume of Truncated Cone

Volume of Truncated Cone is the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Truncated Cone

Base Radius of Truncated Cone

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.

Symbol: r_Base

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Base Radius of Truncated Cone

Top Radius of 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.

Symbol: r_Top

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Top Radius of Truncated Cone

Total Surface Area of Truncated Cone

Total Surface Area of Truncated Cone is the quantity of plane enclosed by the entire surface of the Truncated Cone.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Truncated Cone

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Volume of Truncated Cone

Go Volume of Truncated Cone

V = \frac{π}{3} \cdot h \cdot ({r Base}^{2} + (r Base \cdot r Top) + {r Top}^{2})

Go Volume of Truncated Cone given Curved Surface Area

V = \frac{π}{3} \cdot ({r Base}^{2} + (r Base \cdot r Top) + {r Top}^{2}) \cdot \sqrt{{(\frac{CSA}{π \cdot (r Base + r Top)})}^{2} - {(r Base - r Top)}^{2}}

Go Volume of Truncated Cone given Slant Height

V = \frac{π}{3} \cdot ({r Base}^{2} + (r Base \cdot r Top) + {r Top}^{2}) \cdot \sqrt{{h Slant}^{2} - {(r Base - r Top)}^{2}}

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

Volume of Truncated Cone given Total Surface Area evaluator 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 evaluate 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 evaluate Volume of Truncated Cone given Total Surface Area using this online evaluator? To use this online evaluator 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.

FAQs on Volume of Truncated Cone given Total Surface Area

What is the formula to find Volume of Truncated Cone given Total Surface Area?

The formula of Volume of Truncated Cone given Total Surface Area is expressed as 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). Here is an example- 288.7402 = pi/3*(5^2+(5*2)+2^2)*sqrt(((260-pi*(5^2+2^2))/(pi*(5+2)))^2-(5-2)^2).

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

With Base Radius of Truncated Cone (r_Base), Top Radius of Truncated Cone (r_Top) & Total Surface Area of Truncated Cone (TSA) we can find Volume of Truncated Cone given Total Surface Area using the formula - 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). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Truncated Cone?

Here are the different ways to Calculate Volume of Truncated Cone-

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)

Can the Volume of Truncated Cone given Total Surface Area be negative?

No, the Volume of Truncated Cone given Total Surface Area, measured in Volume cannot be negative.

Which unit is used to measure Volume of Truncated Cone given Total Surface Area?

Volume of Truncated Cone given Total Surface Area is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Truncated Cone given Total Surface Area can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Volume of Truncated Cone given Total Surface Area Formula

​GoVolume of Truncated Cone Formula

​GoVolume of Truncated Cone given Curved Surface Area Formula

Volume of Truncated Cone given Total Surface Area Example

Volume of Truncated Cone given Total Surface Area Solution

Volume of Truncated Cone given Total Surface Area Formula Elements

Other Formulas to find Volume of Truncated Cone

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

FAQs on Volume of Truncated Cone given Total Surface Area

Variable Name

GoVolume of Truncated Cone Formula

GoVolume of Truncated Cone given Curved Surface Area Formula