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Volume of Frustum of Cone Formula

GoVolume of Frustum of Cone given Slant Height Formula

GoVolume of Frustum of Cone given Curved Surface Area Formula

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

V = \frac{1}{3} \cdot π \cdot h \cdot ({r Top}^{2} + {r Base}^{2} + (r Top \cdot r Base))

V - Volume of Frustum of Cone?h - Height of Frustum of Cone?r_Top - Top Radius of Frustum of Cone?r_Base - Base Radius of Frustum of Cone?π - Archimedes' constant?

Volume of Frustum of Cone Example

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Here is how the Volume of Frustum of Cone equation looks like with Values.

Here is how the Volume of Frustum of Cone equation looks like with Units.

Here is how the Volume of Frustum of Cone equation looks like.

1466.0766 = \frac{1}{3} \cdot 3.1416 \cdot 8 \cdot (10^{2} + 5^{2} + (10 \cdot 5))

1466.0766m³ = \frac{1}{3} \cdot 3.1416 \cdot 8m \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))

1466.0766 = \frac{1}{3} \cdot 3.1416 \cdot 8 \cdot (10^{2} + 5^{2} + (10 \cdot 5))

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Volume of Frustum of Cone Solution

Follow our step by step solution on how to calculate Volume of Frustum of Cone?

FIRST Step Consider the formula

V = \frac{1}{3} \cdot π \cdot h \cdot ({r Top}^{2} + {r Base}^{2} + (r Top \cdot r Base))

Next Step Substitute values of Variables

∴

V = \frac{1}{3} \cdot π \cdot 8m \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))

Next Step Substitute values of Constants

∴

V = \frac{1}{3} \cdot 3.1416 \cdot 8m \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))

Next Step Prepare to Evaluate

∴

V = \frac{1}{3} \cdot 3.1416 \cdot 8 \cdot (10^{2} + 5^{2} + (10 \cdot 5))

Next Step Evaluate

∴

V = 1466.07657167524m³

LAST Step Rounding Answer

∴

V = 1466.0766m³

Volume of Frustum of Cone Formula Elements

Variables

Constants

Volume of Frustum of Cone

Volume of Frustum of Cone is the quantity of three-dimensional space enclosed by the entire surface of the Frustum of the Cone.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Frustum of Cone

Height of Frustum of Cone

Height of Frustum of Cone is the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Frustum of Cone

Top Radius of Frustum of Cone

Top Radius of Frustum of Cone is the distance between the center and any point on the circumference of the top circular surface of the Frustum of the Cone.

Symbol: r_Top

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Top Radius of Frustum of Cone

Base Radius of Frustum of Cone

Base Radius of Frustum of Cone is the distance between the center and any point on the circumference of the base circular surface of the Frustum of the Cone.

Symbol: r_Base

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Base Radius of Frustum of 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

Other Formulas to find Volume of Frustum of Cone

Go Volume of Frustum of Cone given Slant Height

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

Go Volume of Frustum of Cone given Curved Surface Area

V = \frac{1}{3} \cdot π \cdot \sqrt{{(\frac{CSA}{π \cdot (r Top + r Base)})}^{2} - {(r Top - r Base)}^{2}} \cdot ({r Top}^{2} + {r Base}^{2} + (r Top \cdot r Base))

Go Volume of Frustum of Cone given Total Surface Area

V = \frac{1}{3} \cdot π \cdot \sqrt{{(\frac{\frac{TSA}{π} - ({r Top}^{2} + {r Base}^{2})}{r Top + r Base})}^{2} - {(r Top - r Base)}^{2}} \cdot ({r Top}^{2} + {r Base}^{2} + (r Top \cdot r Base))

How to Evaluate Volume of Frustum of Cone?

Volume of Frustum of Cone evaluator uses Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone)) to evaluate the Volume of Frustum of Cone, Volume of Frustum of Cone formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone. Volume of Frustum of Cone is denoted by V symbol.

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

FAQs on Volume of Frustum of Cone

What is the formula to find Volume of Frustum of Cone?

The formula of Volume of Frustum of Cone is expressed as Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone)). Here is an example- 1466.077 = 1/3*pi*8*(10^2+5^2+(10*5)).

How to calculate Volume of Frustum of Cone?

With Height of Frustum of Cone (h), Top Radius of Frustum of Cone (r_Top) & Base Radius of Frustum of Cone (r_Base) we can find Volume of Frustum of Cone using the formula - Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone)). This formula also uses Archimedes' constant .

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

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

Volume of Frustum of Cone=(pi*sqrt(Slant Height of Frustum of Cone^2-(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2))/3*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))
Volume of Frustum of Cone=1/3*pi*sqrt((Curved Surface Area of Frustum of Cone/(pi*(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone)))^2-(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))
Volume of Frustum of Cone=1/3*pi*sqrt(((Total Surface Area of Frustum of Cone/pi-(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2))/(Top Radius of Frustum of Cone+Base Radius of Frustum of Cone))^2-(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)*(Top Radius of Frustum of Cone^2+Base Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone*Base Radius of Frustum of Cone))

Can the Volume of Frustum of Cone be negative?

No, the Volume of Frustum of Cone, measured in Volume cannot be negative.

Which unit is used to measure Volume of Frustum of Cone?

Volume of Frustum of Cone 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 Frustum of Cone can be measured.

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Volume of Frustum of Cone Formula

​GoVolume of Frustum of Cone given Slant Height Formula

​GoVolume of Frustum of Cone given Curved Surface Area Formula

Volume of Frustum of Cone Example

Volume of Frustum of Cone Solution

Volume of Frustum of Cone Formula Elements

Other Formulas to find Volume of Frustum of Cone

How to Evaluate Volume of Frustum of Cone?

FAQs on Volume of Frustum of Cone

Variable Name

GoVolume of Frustum of Cone given Slant Height Formula

GoVolume of Frustum of Cone given Curved Surface Area Formula