Volume of Hyperboloid given Skirt Radius Calculator

✖Height of Circular Hyperboloid is the vertical distance between the top and bottom circular faces of the Circular Hyperboloid.ⓘ Height of Circular Hyperboloid [h]			+10% -10%
✖Skirt Radius of Circular Hyperboloid is the distance from center to any point on the circumference of the smallest circular cross-section when cutting Circular Hyperboloid by a horizontal plane.ⓘ Skirt Radius of Circular Hyperboloid [r_Skirt]			+10% -10%
✖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.ⓘ Shape Parameter of Circular Hyperboloid [p]			+10% -10%

✖Volume of Circular Hyperboloid is the amount of three-dimensional space covered by the Circular Hyperboloid.ⓘ Volume of Hyperboloid given Skirt Radius [V]

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Formula

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Volume of Hyperboloid given Skirt Radius

Formula

`"V" = 1/3*pi*"h"*"r"_{"Skirt"}^2*(3+"h"^2/(4*"p"^2))`

Example

`"7462.885m³"=1/3*pi*"12m"*("10m")^2*(3+("12m")^2/(4*("3.5m")^2))`

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Volume of Hyperboloid given Skirt Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
V = 1/3*pi*h*r_Skirt^2*(3+h^2/(4*p^2))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Volume of Circular Hyperboloid - (Measured in Cubic Meter) - Volume of Circular Hyperboloid is the amount of three-dimensional space covered by the Circular Hyperboloid.
Height of Circular Hyperboloid - (Measured in Meter) - Height of Circular Hyperboloid is the vertical distance between the top and bottom circular faces of the Circular Hyperboloid.
Skirt Radius of Circular Hyperboloid - (Measured in Meter) - Skirt Radius of Circular Hyperboloid is the distance from center to any point on the circumference of the smallest circular cross-section when cutting Circular Hyperboloid by a horizontal plane.
Shape Parameter of Circular Hyperboloid - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Height of Circular Hyperboloid: 12 Meter --> 12 Meter No Conversion Required
Skirt Radius of Circular Hyperboloid: 10 Meter --> 10 Meter No Conversion Required
Shape Parameter of Circular Hyperboloid: 3.5 Meter --> 3.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 1/3*pi*h*r_Skirt^2*(3+h^2/(4*p^2)) --> 1/3*pi*12*10^2*(3+12^2/(4*3.5^2))

Evaluating ... ...

V = 7462.88540567045

STEP 3: Convert Result to Output's Unit

7462.88540567045 Cubic Meter --> No Conversion Required

FINAL ANSWER

7462.88540567045 ≈ 7462.885 Cubic Meter <-- Volume of Circular Hyperboloid

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 3D Geometry » Circular Hyperboloid » Height and Volume of Circular Hyperboloid » Volume of Hyperboloid given Skirt Radius

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Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

Divanshi Jain has created this Calculator and 300+ more calculators!

Verified by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has verified this Calculator and 400+ more calculators!

< 6 Height and Volume of Circular Hyperboloid Calculators

Volume of Circular Hyperboloid given Base Radius and Skirt Radius

Go 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 Hyperboloid given Base Radius

Go 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)

Volume of Hyperboloid given Skirt Radius

Go 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))

Height of Circular Hyperboloid

Go Height of Circular Hyperboloid = 2*Shape Parameter of Circular Hyperboloid*sqrt((Base Radius of Circular Hyperboloid^2)/(Skirt Radius of Circular Hyperboloid^2)-1)

Height of Circular Hyperboloid given Volume

Go Height of Circular Hyperboloid = (3*Volume of Circular Hyperboloid)/(pi*((2*Skirt Radius of Circular Hyperboloid^2)+Base Radius of Circular Hyperboloid^2))

Volume of Circular Hyperboloid

Go 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 Hyperboloid given Skirt Radius Formula

What is Circular Hyperboloid?

In geometry, a Hyperboloid of revolution, sometimes called a Circular Hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A Circular Hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings, or more generally, of an affine transformation.

How to Calculate Volume of Hyperboloid given Skirt Radius?

Volume of Hyperboloid given Skirt Radius calculator uses 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)) to calculate the Volume of Circular Hyperboloid, The Volume of Hyperboloid given Skirt Radius formula is defined as the amount of three-dimensional space covered by the Circular Hyperboloid, calculated using skirt radisu of Hyperboloid. Volume of Circular Hyperboloid is denoted by V symbol.

How to calculate Volume of Hyperboloid given Skirt Radius using this online calculator? To use this online calculator for Volume of Hyperboloid given Skirt Radius, enter Height of Circular Hyperboloid (h), Skirt Radius of Circular Hyperboloid (r_Skirt) & Shape Parameter of Circular Hyperboloid (p) and hit the calculate button. Here is how the Volume of Hyperboloid given Skirt Radius calculation can be explained with given input values -> 7462.885 = 1/3*pi*12*10^2*(3+12^2/(4*3.5^2)).

FAQ

What is Volume of Hyperboloid given Skirt Radius?

The Volume of Hyperboloid given Skirt Radius formula is defined as the amount of three-dimensional space covered by the Circular Hyperboloid, calculated using skirt radisu of Hyperboloid and is represented as V = 1/3*pi*h*r_Skirt^2*(3+h^2/(4*p^2)) or 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)). Height of Circular Hyperboloid is the vertical distance between the top and bottom circular faces of the Circular Hyperboloid, Skirt Radius of Circular Hyperboloid is the distance from center to any point on the circumference of the smallest circular cross-section when cutting Circular Hyperboloid by a horizontal plane & 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.

How to calculate Volume of Hyperboloid given Skirt Radius?

The Volume of Hyperboloid given Skirt Radius formula is defined as the amount of three-dimensional space covered by the Circular Hyperboloid, calculated using skirt radisu of Hyperboloid is calculated using 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)). To calculate Volume of Hyperboloid given Skirt Radius, you need Height of Circular Hyperboloid (h), Skirt Radius of Circular Hyperboloid (r_Skirt) & Shape Parameter of Circular Hyperboloid (p). With our tool, you need to enter the respective value for Height of Circular Hyperboloid, Skirt Radius of Circular Hyperboloid & Shape Parameter of Circular Hyperboloid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Circular Hyperboloid?

In this formula, Volume of Circular Hyperboloid uses Height of Circular Hyperboloid, Skirt Radius of Circular Hyperboloid & Shape Parameter of Circular Hyperboloid. We can use 3 other way(s) to calculate the same, which is/are as follows -

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*Base Radius of Circular Hyperboloid^2*(2/(1+Height of Circular Hyperboloid^2/(4*Shape Parameter of Circular Hyperboloid^2))+1)

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