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Volume of Frustum of Cone given Slant Height and Top Area 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{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))

V - Volume of Frustum of Cone?h_Slant - Slant Height of Frustum of Cone?A_Top - Top Area of Frustum of Cone?r_Base - Base Radius of Frustum of Cone?π - Archimedes' constant?

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

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

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

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

1372.3665 = \frac{3.1416 \cdot \sqrt{9^{2} - {(\sqrt{\frac{315}{3.1416}} - 5)}^{2}}}{3} \cdot (\frac{315}{3.1416} + 5^{2} + (\sqrt{\frac{315}{3.1416}} \cdot 5))

1372.3665m³ = \frac{3.1416 \cdot \sqrt{{9m}^{2} - {(\sqrt{\frac{315m²}{3.1416}} - 5m)}^{2}}}{3} \cdot (\frac{315m²}{3.1416} + {5m}^{2} + (\sqrt{\frac{315m²}{3.1416}} \cdot 5m))

1372.3665 = \frac{3.1416 \cdot \sqrt{9^{2} - {(\sqrt{\frac{315}{3.1416}} - 5)}^{2}}}{3} \cdot (\frac{315}{3.1416} + 5^{2} + (\sqrt{\frac{315}{3.1416}} \cdot 5))

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

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

FIRST Step Consider the formula

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))

Next Step Substitute values of Variables

∴

V = \frac{π \cdot \sqrt{{9m}^{2} - {(\sqrt{\frac{315m²}{π}} - 5m)}^{2}}}{3} \cdot (\frac{315m²}{π} + {5m}^{2} + (\sqrt{\frac{315m²}{π}} \cdot 5m))

Next Step Substitute values of Constants

∴

V = \frac{3.1416 \cdot \sqrt{{9m}^{2} - {(\sqrt{\frac{315m²}{3.1416}} - 5m)}^{2}}}{3} \cdot (\frac{315m²}{3.1416} + {5m}^{2} + (\sqrt{\frac{315m²}{3.1416}} \cdot 5m))

Next Step Prepare to Evaluate

∴

V = \frac{3.1416 \cdot \sqrt{9^{2} - {(\sqrt{\frac{315}{3.1416}} - 5)}^{2}}}{3} \cdot (\frac{315}{3.1416} + 5^{2} + (\sqrt{\frac{315}{3.1416}} \cdot 5))

Next Step Evaluate

∴

V = 1372.36654096358m³

LAST Step Rounding Answer

∴

V = 1372.3665m³

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

Top Area of Frustum of Cone is the total amount of two-dimensional space occupied by the top face of the Frustum of the Cone.

Symbol: A_Top

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Top Area 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 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 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))

Go Volume of Frustum of Cone given Base Area and Top Area

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

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

Volume of Frustum of Cone given Slant Height and Top Area evaluator uses 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)) to evaluate the Volume of Frustum of Cone, The Volume of Frustum of Cone given Slant Height and Top Area 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 area 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 and Top Area using this online evaluator? To use this online evaluator for Volume of Frustum of Cone given Slant Height and Top Area, enter Slant Height of Frustum of Cone (h_Slant), Top Area of Frustum of Cone (A_Top) & Base Radius of Frustum of Cone (r_Base) and hit the calculate button.

FAQs on Volume of Frustum of Cone given Slant Height and Top Area

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

The formula of Volume of Frustum of Cone given Slant Height and Top Area is expressed as 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)). Here is an example- 1372.367 = (pi*sqrt(9^2-(sqrt(315/pi)-5)^2))/3*(315/pi+5^2+(sqrt(315/pi)*5)).

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

With Slant Height of Frustum of Cone (h_Slant), Top Area of Frustum of Cone (A_Top) & Base Radius of Frustum of Cone (r_Base) we can find Volume of Frustum of Cone given Slant Height and Top Area using the formula - 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)). 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=(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=1/3*pi*Height of Frustum of Cone*(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 and Top Area be negative?

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

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

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

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

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

Volume of Frustum of Cone given Slant Height and Top Area Formula Elements

Other Formulas to find Volume of Frustum of Cone

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

FAQs on Volume of Frustum of Cone given Slant Height and Top Area

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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