Shape Parameter of Circular Hyperboloid given Volume Calculator

✖Volume of Circular Hyperboloid is the amount of three-dimensional space covered by the Circular Hyperboloid.ⓘ Volume of Circular Hyperboloid [V]			+10% -10%
✖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.ⓘ Base Radius of Circular Hyperboloid [r_Base]			+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 given Volume [p]

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Formula

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Shape Parameter of Circular Hyperboloid given Volume

Formula

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

Example

`"3.468778m"=(3*"7550m³")/(2*pi*sqrt(("20m")^2/("10m")^2-1)*((2*("10m")^2)+("20m")^2))`

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Shape Parameter of Circular Hyperboloid given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shape Parameter of Circular Hyperboloid = (3*Volume of Circular Hyperboloid)/(2*pi*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))
p = (3*V)/(2*pi*sqrt(r_Base^2/r_Skirt^2-1)*((2*r_Skirt^2)+r_Base^2))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

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.
Volume of Circular Hyperboloid - (Measured in Cubic Meter) - Volume of Circular Hyperboloid is the amount of three-dimensional space covered by the Circular Hyperboloid.
Base Radius of Circular Hyperboloid - (Measured in Meter) - 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.
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.

STEP 1: Convert Input(s) to Base Unit

Volume of Circular Hyperboloid: 7550 Cubic Meter --> 7550 Cubic Meter No Conversion Required
Base Radius of Circular Hyperboloid: 20 Meter --> 20 Meter No Conversion Required
Skirt Radius of Circular Hyperboloid: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

p = (3*V)/(2*pi*sqrt(r_Base^2/r_Skirt^2-1)*((2*r_Skirt^2)+r_Base^2)) --> (3*7550)/(2*pi*sqrt(20^2/10^2-1)*((2*10^2)+20^2))

Evaluating ... ...

p = 3.46877763369544

STEP 3: Convert Result to Output's Unit

3.46877763369544 Meter --> No Conversion Required

FINAL ANSWER

3.46877763369544 ≈ 3.468778 Meter <-- Shape Parameter of Circular Hyperboloid

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 3D Geometry » Circular Hyperboloid » Shape Parameter of Circular Hyperboloid » Shape Parameter of Circular Hyperboloid given Volume

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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

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< 2 Shape Parameter of Circular Hyperboloid Calculators

Shape Parameter of Circular Hyperboloid given Volume

Go Shape Parameter of Circular Hyperboloid = (3*Volume of Circular Hyperboloid)/(2*pi*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))

Shape Parameter of Circular Hyperboloid

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

Shape Parameter of Circular Hyperboloid given Volume 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 Shape Parameter of Circular Hyperboloid given Volume?

Shape Parameter of Circular Hyperboloid given Volume calculator uses Shape Parameter of Circular Hyperboloid = (3*Volume of Circular Hyperboloid)/(2*pi*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)) to calculate the Shape Parameter of Circular Hyperboloid, The Shape Parameter of Circular Hyperboloid given Volume formula is defined as the value that determines the shrinkness and flatness of a Circular Hyperboloid depending on its base and skirt radii and height, calculated using volume of Circular Hyperboloid. Shape Parameter of Circular Hyperboloid is denoted by p symbol.

How to calculate Shape Parameter of Circular Hyperboloid given Volume using this online calculator? To use this online calculator for Shape Parameter of Circular Hyperboloid given Volume, enter Volume of Circular Hyperboloid (V), Base Radius of Circular Hyperboloid (r_Base) & Skirt Radius of Circular Hyperboloid (r_Skirt) and hit the calculate button. Here is how the Shape Parameter of Circular Hyperboloid given Volume calculation can be explained with given input values -> 3.468778 = (3*7550)/(2*pi*sqrt(20^2/10^2-1)*((2*10^2)+20^2)).

FAQ

What is Shape Parameter of Circular Hyperboloid given Volume?

The Shape Parameter of Circular Hyperboloid given Volume formula is defined as the value that determines the shrinkness and flatness of a Circular Hyperboloid depending on its base and skirt radii and height, calculated using volume of Circular Hyperboloid and is represented as p = (3*V)/(2*pi*sqrt(r_Base^2/r_Skirt^2-1)*((2*r_Skirt^2)+r_Base^2)) or Shape Parameter of Circular Hyperboloid = (3*Volume of Circular Hyperboloid)/(2*pi*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 is the amount of three-dimensional space covered by the 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 & 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.

How to calculate Shape Parameter of Circular Hyperboloid given Volume?

The Shape Parameter of Circular Hyperboloid given Volume formula is defined as the value that determines the shrinkness and flatness of a Circular Hyperboloid depending on its base and skirt radii and height, calculated using volume of Circular Hyperboloid is calculated using Shape Parameter of Circular Hyperboloid = (3*Volume of Circular Hyperboloid)/(2*pi*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)). To calculate Shape Parameter of Circular Hyperboloid given Volume, you need Volume of Circular Hyperboloid (V), Base Radius of Circular Hyperboloid (r_Base) & Skirt Radius of Circular Hyperboloid (r_Skirt). With our tool, you need to enter the respective value for Volume of Circular Hyperboloid, Base Radius of Circular Hyperboloid & Skirt Radius 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 Shape Parameter of Circular Hyperboloid?

In this formula, Shape Parameter of Circular Hyperboloid uses Volume of Circular Hyperboloid, Base Radius of Circular Hyperboloid & Skirt Radius of Circular Hyperboloid. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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