Volume of Hyperboloid given Base 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%
✖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%
✖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 Base Radius [V]

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Formula

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Volume of Hyperboloid given Base Radius

Formula

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

Example

`"7578.889m³"=1/3*pi*"12m"*("20m")^2*(2/(1+("12m")^2/(4*("3.5m")^2))+1)`

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Volume of Hyperboloid given Base Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
V = 1/3*pi*h*r_Base^2*(2/(1+h^2/(4*p^2))+1)
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.
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.
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
Base Radius of Circular Hyperboloid: 20 Meter --> 20 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_Base^2*(2/(1+h^2/(4*p^2))+1) --> 1/3*pi*12*20^2*(2/(1+12^2/(4*3.5^2))+1)

Evaluating ... ...

V = 7578.88880575859

STEP 3: Convert Result to Output's Unit

7578.88880575859 Cubic Meter --> No Conversion Required

FINAL ANSWER

7578.88880575859 ≈ 7578.889 Cubic Meter <-- Volume 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 » Volume of Hyperboloid given Base Radius

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Created by Divanshi Jain

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

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Verified by Dhruv Walia

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

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< 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 Base 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 Base Radius?

Volume of Hyperboloid given Base Radius calculator 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 calculate 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 calculate Volume of Hyperboloid given Base Radius using this online calculator? To use this online calculator 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. Here is how the Volume of Hyperboloid given Base Radius calculation can be explained with given input values -> 7578.889 = 1/3*pi*12*20^2*(2/(1+12^2/(4*3.5^2))+1).

FAQ

What is Volume of Hyperboloid given Base Radius?

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 and is represented as V = 1/3*pi*h*r_Base^2*(2/(1+h^2/(4*p^2))+1) or 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). Height of Circular Hyperboloid is the vertical distance between the top and bottom circular faces of 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 & 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 Base Radius?

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 is calculated using 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 calculate Volume of Hyperboloid given Base Radius, you need Height of Circular Hyperboloid (h), Base Radius of Circular Hyperboloid (r_Base) & Shape Parameter of Circular Hyperboloid (p). With our tool, you need to enter the respective value for Height of Circular Hyperboloid, Base 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, Base 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*Skirt Radius of Circular Hyperboloid^2*(3+Height of Circular Hyperboloid^2/(4*Shape Parameter of Circular Hyperboloid^2))

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