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Volume of Frustum of Cone given Slant Height Formula

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

V - Volume of Frustum of Cone?h_Slant - Slant 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 given Slant Height Example

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

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

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

1371.3891 = \frac{3.1416 \cdot \sqrt{9^{2} - {(10 - 5)}^{2}}}{3} \cdot (10^{2} + 5^{2} + (10 \cdot 5))

1371.3891m³ = \frac{3.1416 \cdot \sqrt{{9m}^{2} - {(10m - 5m)}^{2}}}{3} \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))

1371.3891 = \frac{3.1416 \cdot \sqrt{9^{2} - {(10 - 5)}^{2}}}{3} \cdot (10^{2} + 5^{2} + (10 \cdot 5))

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3D Geometry » fx Volume of Frustum of Cone given Slant Height

Volume of Frustum of Cone given Slant Height Solution

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

FIRST Step Consider the formula

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))

Next Step Substitute values of Variables

∴

V = \frac{π \cdot \sqrt{{9m}^{2} - {(10m - 5m)}^{2}}}{3} \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))

Next Step Substitute values of Constants

∴

V = \frac{3.1416 \cdot \sqrt{{9m}^{2} - {(10m - 5m)}^{2}}}{3} \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))

Next Step Prepare to Evaluate

∴

V = \frac{3.1416 \cdot \sqrt{9^{2} - {(10 - 5)}^{2}}}{3} \cdot (10^{2} + 5^{2} + (10 \cdot 5))

Next Step Evaluate

∴

V = 1371.38905849622m³

LAST Step Rounding Answer

∴

V = 1371.3891m³

Volume of Frustum of Cone given Slant Height Formula Elements

Variables

Constants

Functions

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

Slant Height of Frustum of Cone

The Slant Height of Frustum of Cone is the length of the line segment joining the extremities of two parallel radii, drawn in the same direction of the two circular bases.

Symbol: h_Slant

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Slant 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

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 Frustum of Cone

Go Volume of Frustum of Cone

V = \frac{1}{3} \cdot π \cdot h \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 given Slant Height?

Volume of Frustum of Cone given Slant Height evaluator uses 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)) to evaluate the Volume of Frustum of Cone, Volume of Frustum of Cone given Slant Height formula is defined as the quantity of three dimensional space enclosed by the entire surface of Frustum of Cone, calculated using the slant height, top radius and base radius of the Frustum of Cone. Volume of Frustum of Cone is denoted by V symbol.

How to evaluate Volume of Frustum of Cone given Slant Height using this online evaluator? To use this online evaluator for Volume of Frustum of Cone given Slant Height, enter Slant Height of Frustum of Cone (h_Slant), 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 given Slant Height

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

The formula of Volume of Frustum of Cone given Slant Height is expressed as 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)). Here is an example- 1371.389 = (pi*sqrt(9^2-(10-5)^2))/3*(10^2+5^2+(10*5)).

How to calculate Volume of Frustum of Cone given Slant Height?

With Slant Height of Frustum of Cone (h_Slant), Top Radius of Frustum of Cone (r_Top) & Base Radius of Frustum of Cone (r_Base) we can find Volume of Frustum of Cone given Slant Height using the formula - 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)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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=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))
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 given Slant Height be negative?

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

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

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

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Volume of Frustum of Cone given Slant Height Formula

​GoVolume of Frustum of Cone Formula

​GoVolume of Frustum of Cone given Curved Surface Area Formula

Volume of Frustum of Cone given Slant Height Example

Volume of Frustum of Cone given Slant Height Solution

Volume of Frustum of Cone given Slant Height Formula Elements

Other Formulas to find Volume of Frustum of Cone

How to Evaluate Volume of Frustum of Cone given Slant Height?

FAQs on Volume of Frustum of Cone given Slant Height

Variable Name

GoVolume of Frustum of Cone Formula

GoVolume of Frustum of Cone given Curved Surface Area Formula