Base Radius 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%
✖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%

✖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 given Volume [r_Base]

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Base Radius of Circular Hyperboloid given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Base Radius of Circular Hyperboloid = sqrt((3*Volume of Circular Hyperboloid)/(pi*Height of Circular Hyperboloid)-(2*Skirt Radius of Circular Hyperboloid^2))
r_Base = sqrt((3*V)/(pi*h)-(2*r_Skirt^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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Volume of Circular Hyperboloid: 7550 Cubic Meter --> 7550 Cubic Meter No Conversion Required
Height of Circular Hyperboloid: 12 Meter --> 12 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

r_Base = sqrt((3*V)/(pi*h)-(2*r_Skirt^2)) --> sqrt((3*7550)/(pi*12)-(2*10^2))

Evaluating ... ...

r_Base = 20.0202375153719

STEP 3: Convert Result to Output's Unit

20.0202375153719 Meter --> No Conversion Required

FINAL ANSWER

20.0202375153719 ≈ 20.02024 Meter <-- Base Radius of Circular Hyperboloid

(Calculation completed in 00.004 seconds)

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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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< Radius of Hyperboloid Calculators

Skirt Radius of Circular Hyperboloid given Volume

LaTeX Go Skirt Radius of Circular Hyperboloid = sqrt(1/2*((3*Volume of Circular Hyperboloid)/(pi*Height of Circular Hyperboloid)-Base Radius of Circular Hyperboloid^2))

Base Radius of Circular Hyperboloid given Volume

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

Skirt Radius of Circular Hyperboloid

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

Base Radius of Circular Hyperboloid

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

Base Radius of Circular Hyperboloid given Volume Formula

LaTeX Go

Base Radius of Circular Hyperboloid = sqrt((3*Volume of Circular Hyperboloid)/(pi*Height of Circular Hyperboloid)-(2*Skirt Radius of Circular Hyperboloid^2))
r_Base = sqrt((3*V)/(pi*h)-(2*r_Skirt^2))

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 Base Radius of Circular Hyperboloid given Volume?

Base Radius of Circular Hyperboloid given Volume calculator uses Base Radius of Circular Hyperboloid = sqrt((3*Volume of Circular Hyperboloid)/(pi*Height of Circular Hyperboloid)-(2*Skirt Radius of Circular Hyperboloid^2)) to calculate the Base Radius of Circular Hyperboloid, The Base Radius of Circular Hyperboloid given Volume formula is defined as the distance from the center to any point on the circumference of the circular face at the bottom of the Circular Hyperboloid, calculated using volume of Circular Hyperboloid. Base Radius of Circular Hyperboloid is denoted by r_Base symbol.

How to calculate Base Radius of Circular Hyperboloid given Volume using this online calculator? To use this online calculator for Base Radius of Circular Hyperboloid given Volume, enter Volume of Circular Hyperboloid (V), Height of Circular Hyperboloid (h) & Skirt Radius of Circular Hyperboloid (r_Skirt) and hit the calculate button. Here is how the Base Radius of Circular Hyperboloid given Volume calculation can be explained with given input values -> 20.02024 = sqrt((3*7550)/(pi*12)-(2*10^2)).

FAQ

What is Base Radius of Circular Hyperboloid given Volume?

The Base Radius of Circular Hyperboloid given Volume formula is defined as the distance from the center to any point on the circumference of the circular face at the bottom of the Circular Hyperboloid, calculated using volume of Circular Hyperboloid and is represented as r_Base = sqrt((3*V)/(pi*h)-(2*r_Skirt^2)) or Base Radius of Circular Hyperboloid = sqrt((3*Volume of Circular Hyperboloid)/(pi*Height of Circular Hyperboloid)-(2*Skirt Radius of Circular Hyperboloid^2)). Volume of Circular Hyperboloid is the amount of three-dimensional space covered by the Circular Hyperboloid, 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.

How to calculate Base Radius of Circular Hyperboloid given Volume?

The Base Radius of Circular Hyperboloid given Volume formula is defined as the distance from the center to any point on the circumference of the circular face at the bottom of the Circular Hyperboloid, calculated using volume of Circular Hyperboloid is calculated using Base Radius of Circular Hyperboloid = sqrt((3*Volume of Circular Hyperboloid)/(pi*Height of Circular Hyperboloid)-(2*Skirt Radius of Circular Hyperboloid^2)). To calculate Base Radius of Circular Hyperboloid given Volume, you need Volume of Circular Hyperboloid (V), Height of Circular Hyperboloid (h) & Skirt Radius of Circular Hyperboloid (r_Skirt). With our tool, you need to enter the respective value for Volume of Circular Hyperboloid, Height 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 Base Radius of Circular Hyperboloid?

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

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

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