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Volume of Frustum of Cone given Slant Height, Height and Top Radius Formula

GoVolume of Frustum of Cone given Slant Height and Base Area Formula

GoVolume of Frustum of Cone given Slant Height, Base Area and Top 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 Top - \sqrt{{h Slant}^{2} - h^{2}})}^{2} + (r Top \cdot (r Top - \sqrt{{h Slant}^{2} - h^{2}})))

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

Volume of Frustum of Cone given Slant Height, Height and Top Radius Example

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

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

Here is how the Volume of Frustum of Cone given Slant Height, Height and Top Radius equation looks like.

1619.4435 = \frac{1}{3} \cdot 3.1416 \cdot 8 \cdot (10^{2} + {(10 - \sqrt{9^{2} - 8^{2}})}^{2} + (10 \cdot (10 - \sqrt{9^{2} - 8^{2}})))

1619.4435m³ = \frac{1}{3} \cdot 3.1416 \cdot 8m \cdot ({10m}^{2} + {(10m - \sqrt{{9m}^{2} - {8m}^{2}})}^{2} + (10m \cdot (10m - \sqrt{{9m}^{2} - {8m}^{2}})))

1619.4435 = \frac{1}{3} \cdot 3.1416 \cdot 8 \cdot (10^{2} + {(10 - \sqrt{9^{2} - 8^{2}})}^{2} + (10 \cdot (10 - \sqrt{9^{2} - 8^{2}})))

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3D Geometry » fx Volume of Frustum of Cone given Slant Height, Height and Top Radius

Volume of Frustum of Cone given Slant Height, Height and Top Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{1}{3} \cdot π \cdot 8m \cdot ({10m}^{2} + {(10m - \sqrt{{9m}^{2} - {8m}^{2}})}^{2} + (10m \cdot (10m - \sqrt{{9m}^{2} - {8m}^{2}})))

Next Step Substitute values of Constants

∴

V = \frac{1}{3} \cdot 3.1416 \cdot 8m \cdot ({10m}^{2} + {(10m - \sqrt{{9m}^{2} - {8m}^{2}})}^{2} + (10m \cdot (10m - \sqrt{{9m}^{2} - {8m}^{2}})))

Next Step Prepare to Evaluate

∴

V = \frac{1}{3} \cdot 3.1416 \cdot 8 \cdot (10^{2} + {(10 - \sqrt{9^{2} - 8^{2}})}^{2} + (10 \cdot (10 - \sqrt{9^{2} - 8^{2}})))

Next Step Evaluate

∴

V = 1619.44352236136m³

LAST Step Rounding Answer

∴

V = 1619.4435m³

Volume of Frustum of Cone given Slant Height, Height and Top Radius 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

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

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

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 given Slant Height and Base Area

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

Go Volume of Frustum of Cone given Slant Height, Base Area and Top Area

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

Go Volume of Frustum of Cone given Slant Height and Top Area

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

Go Volume of Frustum of Cone given Top Area

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

How to Evaluate Volume of Frustum of Cone given Slant Height, Height and Top Radius?

Volume of Frustum of Cone given Slant Height, Height and Top Radius evaluator uses Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)))) to evaluate the Volume of Frustum of Cone, The Volume of Frustum of Cone given Slant Height, Height and Top Radius 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 height 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, Height and Top Radius using this online evaluator? To use this online evaluator for Volume of Frustum of Cone given Slant Height, Height and Top Radius, enter Height of Frustum of Cone (h), Top Radius of Frustum of Cone (r_Top) & Slant Height of Frustum of Cone (h_Slant) and hit the calculate button.

FAQs on Volume of Frustum of Cone given Slant Height, Height and Top Radius

What is the formula to find Volume of Frustum of Cone given Slant Height, Height and Top Radius?

The formula of Volume of Frustum of Cone given Slant Height, Height and Top Radius is expressed as Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)))). Here is an example- 1619.444 = 1/3*pi*8*(10^2+(10-sqrt(9^2-8^2))^2+(10*(10-sqrt(9^2-8^2)))).

How to calculate Volume of Frustum of Cone given Slant Height, Height and Top Radius?

With Height of Frustum of Cone (h), Top Radius of Frustum of Cone (r_Top) & Slant Height of Frustum of Cone (h_Slant) we can find Volume of Frustum of Cone given Slant Height, Height and Top Radius using the formula - Volume of Frustum of Cone = 1/3*pi*Height of Frustum of Cone*(Top Radius of Frustum of Cone^2+(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2))^2+(Top Radius of Frustum of Cone*(Top Radius of Frustum of Cone-sqrt(Slant Height of Frustum of Cone^2-Height of Frustum of Cone^2)))). This formula also uses Archimedes' constant and Square Root Function 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=(pi*sqrt(Slant Height of Frustum of Cone^2-(Top Radius of Frustum of Cone-sqrt(Base Area of Frustum of Cone/pi))^2))/3*(Top Radius of Frustum of Cone^2+Base Area of Frustum of Cone/pi+(Top Radius of Frustum of Cone*sqrt(Base Area of Frustum of Cone/pi)))
Volume of Frustum of Cone=(pi*sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-sqrt(Base Area of Frustum of Cone/pi))^2))/3*(Top Area of Frustum of Cone/pi+Base Area of Frustum of Cone/pi+(sqrt(Top Area of Frustum of Cone/pi)*sqrt(Base Area of Frustum of Cone/pi)))
Volume of Frustum of Cone=(pi*sqrt(Slant Height of Frustum of Cone^2-(sqrt(Top Area of Frustum of Cone/pi)-Base Radius of Frustum of Cone)^2))/3*(Top Area of Frustum of Cone/pi+Base Radius of Frustum of Cone^2+(sqrt(Top Area of Frustum of Cone/pi)*Base Radius of Frustum of Cone))

Can the Volume of Frustum of Cone given Slant Height, Height and Top Radius be negative?

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

Which unit is used to measure Volume of Frustum of Cone given Slant Height, Height and Top Radius?

Volume of Frustum of Cone given Slant Height, Height and Top Radius 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, Height and Top Radius can be measured.

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Volume of Frustum of Cone given Slant Height, Height and Top Radius Formula

​GoVolume of Frustum of Cone given Slant Height and Base Area Formula

​GoVolume of Frustum of Cone given Slant Height, Base Area and Top Area Formula

Volume of Frustum of Cone given Slant Height, Height and Top Radius Example

Volume of Frustum of Cone given Slant Height, Height and Top Radius Solution

Volume of Frustum of Cone given Slant Height, Height and Top Radius Formula Elements

Other Formulas to find Volume of Frustum of Cone

How to Evaluate Volume of Frustum of Cone given Slant Height, Height and Top Radius?

FAQs on Volume of Frustum of Cone given Slant Height, Height and Top Radius

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GoVolume of Frustum of Cone given Slant Height and Base Area Formula

GoVolume of Frustum of Cone given Slant Height, Base Area and Top Area Formula