Height of Circular Hyperboloid Calculator

✖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%
✖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%

✖Height of Circular Hyperboloid is the vertical distance between the top and bottom circular faces of the Circular Hyperboloid.ⓘ Height of Circular Hyperboloid [h]

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Formula

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Height of Circular Hyperboloid

Formula

`"h" = 2*"p"*sqrt(("r"_{"Base"}^2)/("r"_{"Skirt"}^2)-1)`

Example

`"12.12436m"=2*"3.5m"*sqrt((("20m")^2)/(("10m")^2)-1)`

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Height of Circular Hyperboloid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Circular Hyperboloid = 2*Shape Parameter of Circular Hyperboloid*sqrt((Base Radius of Circular Hyperboloid^2)/(Skirt Radius of Circular Hyperboloid^2)-1)
h = 2*p*sqrt((r_Base^2)/(r_Skirt^2)-1)
This formula uses 1 Functions, 4 Variables

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

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.
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.
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

Shape Parameter of Circular Hyperboloid: 3.5 Meter --> 3.5 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

h = 2*p*sqrt((r_Base^2)/(r_Skirt^2)-1) --> 2*3.5*sqrt((20^2)/(10^2)-1)

Evaluating ... ...

h = 12.1243556529821

STEP 3: Convert Result to Output's Unit

12.1243556529821 Meter --> No Conversion Required

FINAL ANSWER

12.1243556529821 ≈ 12.12436 Meter <-- Height of Circular Hyperboloid

(Calculation completed in 00.004 seconds)

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

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ 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)

Height of Circular Hyperboloid 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 Height of Circular Hyperboloid?

Height of Circular Hyperboloid calculator uses Height of Circular Hyperboloid = 2*Shape Parameter of Circular Hyperboloid*sqrt((Base Radius of Circular Hyperboloid^2)/(Skirt Radius of Circular Hyperboloid^2)-1) to calculate the Height of Circular Hyperboloid, Height of Circular Hyperboloid formula is defined as the vertical distance between the top and bottom circular faces of the Circular Hyperboloid. Height of Circular Hyperboloid is denoted by h symbol.

How to calculate Height of Circular Hyperboloid using this online calculator? To use this online calculator for Height of Circular Hyperboloid, enter Shape Parameter of Circular Hyperboloid (p), Base Radius of Circular Hyperboloid (r_Base) & Skirt Radius of Circular Hyperboloid (r_Skirt) and hit the calculate button. Here is how the Height of Circular Hyperboloid calculation can be explained with given input values -> 12.12436 = 2*3.5*sqrt((20^2)/(10^2)-1).

FAQ

What is Height of Circular Hyperboloid?

Height of Circular Hyperboloid formula is defined as the vertical distance between the top and bottom circular faces of the Circular Hyperboloid and is represented as h = 2*p*sqrt((r_Base^2)/(r_Skirt^2)-1) or Height of Circular Hyperboloid = 2*Shape Parameter of Circular Hyperboloid*sqrt((Base Radius of Circular Hyperboloid^2)/(Skirt Radius of Circular Hyperboloid^2)-1). 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, 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 Height of Circular Hyperboloid?

Height of Circular Hyperboloid formula is defined as the vertical distance between the top and bottom circular faces of the Circular Hyperboloid is calculated using Height of Circular Hyperboloid = 2*Shape Parameter of Circular Hyperboloid*sqrt((Base Radius of Circular Hyperboloid^2)/(Skirt Radius of Circular Hyperboloid^2)-1). To calculate Height of Circular Hyperboloid, you need Shape Parameter of Circular Hyperboloid (p), 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 Shape Parameter 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 Height of Circular Hyperboloid?

In this formula, Height of Circular Hyperboloid uses Shape Parameter 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 -

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

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