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Volume of Hyperboloid given Base Radius Formula

GoVolume of Circular Hyperboloid Formula

GoVolume of Circular Hyperboloid given Base Radius and Skirt Radius Formula

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Volume of Circular Hyperboloid is the amount of three-dimensional space covered by the Circular Hyperboloid. Check FAQs

V = \frac{1}{3} \cdot π \cdot h \cdot {r Base}^{2} \cdot (\frac{2}{1 + \frac{h^{2}}{4 \cdot p^{2}}} + 1)

V - Volume of Circular Hyperboloid?h - Height of Circular Hyperboloid?r_Base - Base Radius of Circular Hyperboloid?p - Shape Parameter of Circular Hyperboloid?π - Archimedes' constant?

Volume of Hyperboloid given Base Radius Example

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Here is how the Volume of Hyperboloid given Base Radius equation looks like with Values.

Here is how the Volume of Hyperboloid given Base Radius equation looks like with Units.

Here is how the Volume of Hyperboloid given Base Radius equation looks like.

7578.8888 = \frac{1}{3} \cdot 3.1416 \cdot 12 \cdot 20^{2} \cdot (\frac{2}{1 + \frac{12^{2}}{4 \cdot {3.5}^{2}}} + 1)

7578.8888m³ = \frac{1}{3} \cdot 3.1416 \cdot 12m \cdot {20m}^{2} \cdot (\frac{2}{1 + \frac{{12m}^{2}}{4 \cdot {3.5m}^{2}}} + 1)

7578.8888 = \frac{1}{3} \cdot 3.1416 \cdot 12 \cdot 20^{2} \cdot (\frac{2}{1 + \frac{12^{2}}{4 \cdot {3.5}^{2}}} + 1)

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Volume of Hyperboloid given Base Radius Solution

Follow our step by step solution on how to calculate Volume of Hyperboloid given Base Radius?

FIRST Step Consider the formula

V = \frac{1}{3} \cdot π \cdot h \cdot {r Base}^{2} \cdot (\frac{2}{1 + \frac{h^{2}}{4 \cdot p^{2}}} + 1)

Next Step Substitute values of Variables

∴

V = \frac{1}{3} \cdot π \cdot 12m \cdot {20m}^{2} \cdot (\frac{2}{1 + \frac{{12m}^{2}}{4 \cdot {3.5m}^{2}}} + 1)

Next Step Substitute values of Constants

∴

V = \frac{1}{3} \cdot 3.1416 \cdot 12m \cdot {20m}^{2} \cdot (\frac{2}{1 + \frac{{12m}^{2}}{4 \cdot {3.5m}^{2}}} + 1)

Next Step Prepare to Evaluate

∴

V = \frac{1}{3} \cdot 3.1416 \cdot 12 \cdot 20^{2} \cdot (\frac{2}{1 + \frac{12^{2}}{4 \cdot {3.5}^{2}}} + 1)

Next Step Evaluate

∴

V = 7578.88880575859m³

LAST Step Rounding Answer

∴

V = 7578.8888m³

Volume of Hyperboloid given Base Radius Formula Elements

Variables

Constants

Volume of Circular Hyperboloid

Volume of Circular Hyperboloid is the amount of three-dimensional space covered by the Circular Hyperboloid.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Circular Hyperboloid

Height of Circular Hyperboloid

Height of Circular Hyperboloid is the vertical distance between the top and bottom circular faces of the Circular Hyperboloid.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Circular Hyperboloid

Base Radius of Circular Hyperboloid

Base Radius of Circular Hyperboloid is the distance from the center to any point on the circumference of the circular face at the bottom of the Circular Hyperboloid.

Symbol: r_Base

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Base Radius of Circular Hyperboloid

Shape Parameter of Circular Hyperboloid

Shape Parameter of Circular Hyperboloid is the value that determines the shrinkness and flatness of a Circular Hyperboloid depending on its base and skirt radii and height.

Symbol: p

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Shape Parameter of Circular Hyperboloid

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 Circular Hyperboloid

Go Volume of Circular Hyperboloid

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

Go Volume of Circular Hyperboloid given Base Radius and Skirt Radius

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

Go Volume of Hyperboloid given Skirt Radius

V = \frac{1}{3} \cdot π \cdot h \cdot {r Skirt}^{2} \cdot (3 + \frac{h^{2}}{4 \cdot p^{2}})

Other formulas in Height and Volume of Circular Hyperboloid category

Go Height of Circular Hyperboloid

h = 2 \cdot p \cdot \sqrt{\frac{{r Base}^{2}}{{r Skirt}^{2}} - 1}

Go Height of Circular Hyperboloid given Volume

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

How to Evaluate Volume of Hyperboloid given Base Radius?

Volume of Hyperboloid given Base Radius evaluator uses Volume of Circular Hyperboloid = 1/3*pi*Height of Circular Hyperboloid*Base Radius of Circular Hyperboloid^2*(2/(1+Height of Circular Hyperboloid^2/(4*Shape Parameter of Circular Hyperboloid^2))+1) to evaluate the Volume of Circular Hyperboloid, The Volume of Hyperboloid given Base Radius formula is defined as the amount of three-dimensional space covered by the Circular Hyperboloid, calculated using base radius of Circular Hyperboloid. Volume of Circular Hyperboloid is denoted by V symbol.

How to evaluate Volume of Hyperboloid given Base Radius using this online evaluator? To use this online evaluator for Volume of Hyperboloid given Base Radius, enter Height of Circular Hyperboloid (h), Base Radius of Circular Hyperboloid (r_Base) & Shape Parameter of Circular Hyperboloid (p) and hit the calculate button.

FAQs on Volume of Hyperboloid given Base Radius

What is the formula to find Volume of Hyperboloid given Base Radius?

The formula of Volume of Hyperboloid given Base Radius is expressed as Volume of Circular Hyperboloid = 1/3*pi*Height of Circular Hyperboloid*Base Radius of Circular Hyperboloid^2*(2/(1+Height of Circular Hyperboloid^2/(4*Shape Parameter of Circular Hyperboloid^2))+1). Here is an example- 7578.889 = 1/3*pi*12*20^2*(2/(1+12^2/(4*3.5^2))+1).

How to calculate Volume of Hyperboloid given Base Radius?

With Height of Circular Hyperboloid (h), Base Radius of Circular Hyperboloid (r_Base) & Shape Parameter of Circular Hyperboloid (p) we can find Volume of Hyperboloid given Base Radius using the formula - Volume of Circular Hyperboloid = 1/3*pi*Height of Circular Hyperboloid*Base Radius of Circular Hyperboloid^2*(2/(1+Height of Circular Hyperboloid^2/(4*Shape Parameter of Circular Hyperboloid^2))+1). This formula also uses Archimedes' constant .

What are the other ways to Calculate Volume of Circular Hyperboloid?

Here are the different ways to Calculate Volume of Circular Hyperboloid-

Volume of Circular Hyperboloid=1/3*pi*Height of Circular Hyperboloid*((2*Skirt Radius of Circular Hyperboloid^2)+Base Radius of Circular Hyperboloid^2)
Volume of Circular Hyperboloid=2/3*pi*Shape Parameter of Circular Hyperboloid*sqrt((Base Radius of Circular Hyperboloid^2)/(Skirt Radius of Circular Hyperboloid^2)-1)*((2*Skirt Radius of Circular Hyperboloid^2)+Base Radius of Circular Hyperboloid^2)
Volume of Circular Hyperboloid=1/3*pi*Height of Circular Hyperboloid*Skirt Radius of Circular Hyperboloid^2*(3+Height of Circular Hyperboloid^2/(4*Shape Parameter of Circular Hyperboloid^2))

Can the Volume of Hyperboloid given Base Radius be negative?

No, the Volume of Hyperboloid given Base Radius, measured in Volume cannot be negative.

Which unit is used to measure Volume of Hyperboloid given Base Radius?

Volume of Hyperboloid given Base 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 Hyperboloid given Base Radius can be measured.

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Volume of Hyperboloid given Base Radius Formula

​GoVolume of Circular Hyperboloid Formula

​GoVolume of Circular Hyperboloid given Base Radius and Skirt Radius Formula

Volume of Hyperboloid given Base Radius Example

Volume of Hyperboloid given Base Radius Solution

Volume of Hyperboloid given Base Radius Formula Elements

Other Formulas to find Volume of Circular Hyperboloid

Other formulas in Height and Volume of Circular Hyperboloid category

How to Evaluate Volume of Hyperboloid given Base Radius?

FAQs on Volume of Hyperboloid given Base Radius

Variable Name

GoVolume of Circular Hyperboloid Formula

GoVolume of Circular Hyperboloid given Base Radius and Skirt Radius Formula