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 Slant Height Formula

GoVolume of Truncated Cone Formula

GoVolume of Truncated Cone given Total 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{{h Slant}^{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?h_Slant - Slant Height of Truncated Cone?π - Archimedes' constant?

Volume of Truncated Cone given Slant Height Example

With values

With units

Only example

Here is how the Volume of Truncated Cone given Slant Height equation looks like with Values.

Here is how the Volume of Truncated Cone given Slant Height equation looks like with Units.

Here is how the Volume of Truncated Cone given Slant Height equation looks like.

302.8828 = \frac{3.1416}{3} \cdot (5^{2} + (5 \cdot 2) + 2^{2}) \cdot \sqrt{8^{2} - {(5 - 2)}^{2}}

302.8828m³ = \frac{3.1416}{3} \cdot ({5m}^{2} + (5m \cdot 2m) + {2m}^{2}) \cdot \sqrt{{8m}^{2} - {(5m - 2m)}^{2}}

302.8828 = \frac{3.1416}{3} \cdot (5^{2} + (5 \cdot 2) + 2^{2}) \cdot \sqrt{8^{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 Slant Height

Volume of Truncated Cone given Slant Height Solution

Follow our step by step solution on how to calculate Volume of Truncated Cone given Slant Height?

FIRST Step Consider the formula

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}}

Next Step Substitute values of Variables

∴

V = \frac{π}{3} \cdot ({5m}^{2} + (5m \cdot 2m) + {2m}^{2}) \cdot \sqrt{{8m}^{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{{8m}^{2} - {(5m - 2m)}^{2}}

Next Step Prepare to Evaluate

∴

V = \frac{3.1416}{3} \cdot (5^{2} + (5 \cdot 2) + 2^{2}) \cdot \sqrt{8^{2} - {(5 - 2)}^{2}}

Next Step Evaluate

∴

V = 302.882770900105m³

LAST Step Rounding Answer

∴

V = 302.8828m³

Volume of Truncated Cone given Slant Height 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

Slant Height of Truncated Cone

Slant Height of Truncated Cone is the length of the straight line connecting any point on the base to the truncated top circular face of the Truncated Cone.

Symbol: h_Slant

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Slant Height 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 Total Surface Area

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}}

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}}

How to Evaluate Volume of Truncated Cone given Slant Height?

Volume of Truncated Cone given Slant Height 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(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2) to evaluate the Volume of Truncated Cone, The Volume of Truncated Cone given Slant Height formula is defined as the total quantity of three dimensional space enclosed by the entire surface of the Truncated Cone, and calculated using the slant height of Truncated Cone. Volume of Truncated Cone is denoted by V symbol.

How to evaluate Volume of Truncated Cone given Slant Height using this online evaluator? To use this online evaluator for Volume of Truncated Cone given Slant Height, enter Base Radius of Truncated Cone (r_Base), Top Radius of Truncated Cone (r_Top) & Slant Height of Truncated Cone (h_Slant) and hit the calculate button.

FAQs on Volume of Truncated Cone given Slant Height

What is the formula to find Volume of Truncated Cone given Slant Height?

The formula of Volume of Truncated Cone given Slant Height 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(Slant Height of Truncated Cone^2-(Base Radius of Truncated Cone-Top Radius of Truncated Cone)^2). Here is an example- 302.8828 = pi/3*(5^2+(5*2)+2^2)*sqrt(8^2-(5-2)^2).

How to calculate Volume of Truncated Cone given Slant Height?

With Base Radius of Truncated Cone (r_Base), Top Radius of Truncated Cone (r_Top) & Slant Height of Truncated Cone (h_Slant) we can find Volume of Truncated Cone given Slant Height 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(Slant Height 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(((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=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)

Can the Volume of Truncated Cone given Slant Height be negative?

No, the Volume of Truncated Cone given Slant Height, measured in Volume cannot be negative.

Which unit is used to measure Volume of Truncated Cone given Slant Height?

Volume of Truncated Cone given Slant Height 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 Slant Height can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Volume of Truncated Cone given Slant Height Formula

​GoVolume of Truncated Cone Formula

​GoVolume of Truncated Cone given Total Surface Area Formula

Volume of Truncated Cone given Slant Height Example

Volume of Truncated Cone given Slant Height Solution

Volume of Truncated Cone given Slant Height Formula Elements

Other Formulas to find Volume of Truncated Cone

How to Evaluate Volume of Truncated Cone given Slant Height?

FAQs on Volume of Truncated Cone given Slant Height

Variable Name

GoVolume of Truncated Cone Formula

GoVolume of Truncated Cone given Total Surface Area Formula