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Height of Frustum of Cone given Volume Formula

GoHeight of Frustum of Cone given Slant Height Formula

GoHeight of Frustum of Cone given Curved Surface Area Formula

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

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

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

Height of Frustum of Cone given Volume Example

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

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

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

8.1851 = \frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))}

8.1851m = \frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))}

8.1851 = \frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))}

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Height of Frustum of Cone given Volume Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = \frac{3 \cdot 1500m³}{π \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))}

Next Step Substitute values of Constants

∴

h = \frac{3 \cdot 1500m³}{3.1416 \cdot ({10m}^{2} + {5m}^{2} + (10m \cdot 5m))}

Next Step Prepare to Evaluate

∴

h = \frac{3 \cdot 1500}{3.1416 \cdot (10^{2} + 5^{2} + (10 \cdot 5))}

Next Step Evaluate

∴

h = 8.18511135901176m

LAST Step Rounding Answer

∴

h = 8.1851m

Height of Frustum of Cone given Volume Formula Elements

Variables

Constants

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

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

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 Height of Frustum of Cone

Go Height of Frustum of Cone given Slant Height

h = \sqrt{{h Slant}^{2} - {(r Top - r Base)}^{2}}

Go Height of Frustum of Cone given Curved Surface Area

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

Go Height of Frustum of Cone given Total Surface Area

h = \sqrt{{(\frac{\frac{TSA}{π} - ({r Top}^{2} + {r Base}^{2})}{r Top + r Base})}^{2} - {(r Top - r Base)}^{2}}

How to Evaluate Height of Frustum of Cone given Volume?

Height of Frustum of Cone given Volume evaluator uses Height of Frustum of Cone = (3*Volume 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))) to evaluate the Height of Frustum of Cone, The Height of Frustum of Cone given Volume formula is defined as the maximum vertical distance from the bottom to the top circular face of the Frustum of the Cone and calculated using the volume, top radius, and base radius of the Frustum of Cone. Height of Frustum of Cone is denoted by h symbol.

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

FAQs on Height of Frustum of Cone given Volume

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

The formula of Height of Frustum of Cone given Volume is expressed as Height of Frustum of Cone = (3*Volume 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))). Here is an example- 8.185111 = (3*1500)/(pi*(10^2+5^2+(10*5))).

How to calculate Height of Frustum of Cone given Volume?

With Volume of Frustum of Cone (V), Top Radius of Frustum of Cone (r_Top) & Base Radius of Frustum of Cone (r_Base) we can find Height of Frustum of Cone given Volume using the formula - Height of Frustum of Cone = (3*Volume 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))). This formula also uses Archimedes' constant .

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

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

Height of Frustum of Cone=sqrt(Slant Height of Frustum of Cone^2-(Top Radius of Frustum of Cone-Base Radius of Frustum of Cone)^2)
Height of Frustum of Cone=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)
Height of Frustum of Cone=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)

Can the Height of Frustum of Cone given Volume be negative?

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

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

Height of Frustum of Cone given Volume is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Frustum of Cone given Volume can be measured.

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Height of Frustum of Cone given Volume Formula

​GoHeight of Frustum of Cone given Slant Height Formula

​GoHeight of Frustum of Cone given Curved Surface Area Formula

Height of Frustum of Cone given Volume Example

Height of Frustum of Cone given Volume Solution

Height of Frustum of Cone given Volume Formula Elements

Other Formulas to find Height of Frustum of Cone

How to Evaluate Height of Frustum of Cone given Volume?

FAQs on Height of Frustum of Cone given Volume

Variable Name

GoHeight of Frustum of Cone given Slant Height Formula

GoHeight of Frustum of Cone given Curved Surface Area Formula