Radius of Paraboloid given Lateral Surface Area Calculator

✖Shape Parameter of Paraboloid is the total length of the boundary or outer edge of Paraboloid.ⓘ Shape Parameter of Paraboloid [p]			+10% -10%
✖Lateral Surface Area of Paraboloid is the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid.ⓘ Lateral Surface Area of Paraboloid [LSA]			+10% -10%

✖Radius of Paraboloid is defined as the length of the straight line from the center to any point on the circumference of the circular face of the Paraboloid.ⓘ Radius of Paraboloid given Lateral Surface Area [r]

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Formula

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Radius of Paraboloid given Lateral Surface Area

Formula

`"r" = 1/(2*"p")*sqrt(((6*"LSA"*"p"^2)/pi+1)^(2/3)-1)`

Example

`"4.998416m"=1/(2*"2")*sqrt(((6*"1050m²"*("2")^2)/pi+1)^(2/3)-1)`

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Radius of Paraboloid given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Paraboloid = 1/(2*Shape Parameter of Paraboloid)*sqrt(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)
r = 1/(2*p)*sqrt(((6*LSA*p^2)/pi+1)^(2/3)-1)
This formula uses 1 Constants, 1 Functions, 3 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

Radius of Paraboloid - (Measured in Meter) - Radius of Paraboloid is defined as the length of the straight line from the center to any point on the circumference of the circular face of the Paraboloid.
Shape Parameter of Paraboloid - Shape Parameter of Paraboloid is the total length of the boundary or outer edge of Paraboloid.
Lateral Surface Area of Paraboloid - (Measured in Square Meter) - Lateral Surface Area of Paraboloid is the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid.

STEP 1: Convert Input(s) to Base Unit

Shape Parameter of Paraboloid: 2 --> No Conversion Required
Lateral Surface Area of Paraboloid: 1050 Square Meter --> 1050 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = 1/(2*p)*sqrt(((6*LSA*p^2)/pi+1)^(2/3)-1) --> 1/(2*2)*sqrt(((6*1050*2^2)/pi+1)^(2/3)-1)

Evaluating ... ...

r = 4.99841614142601

STEP 3: Convert Result to Output's Unit

4.99841614142601 Meter --> No Conversion Required

FINAL ANSWER

4.99841614142601 ≈ 4.998416 Meter <-- Radius of Paraboloid

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Paraboloid » Radius of Paraboloid » Radius of Paraboloid given Lateral Surface Area

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Created by Divanshi Jain

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

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

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< 5 Radius of Paraboloid Calculators

Radius of Paraboloid formula given Surface to Volume Ratio

Go Radius of Paraboloid = sqrt(Lateral Surface Area of Paraboloid/((1/2*Surface to Volume Ratio of Paraboloid*pi*Height of Paraboloid)-pi))

Radius of Paraboloid given Lateral Surface Area

Go Radius of Paraboloid = 1/(2*Shape Parameter of Paraboloid)*sqrt(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)

Radius of Paraboloid given Total Surface Area and Lateral Surface Area

Go Radius of Paraboloid = sqrt((Total Surface Area of Paraboloid-Lateral Surface Area of Paraboloid)/pi)

Radius of Paraboloid given Volume

Go Radius of Paraboloid = sqrt((2*Volume of Paraboloid)/(pi*Height of Paraboloid))

Radius of Paraboloid

Go Radius of Paraboloid = sqrt(Height of Paraboloid/Shape Parameter of Paraboloid)

Radius of Paraboloid given Lateral Surface Area Formula

Radius of Paraboloid = 1/(2*Shape Parameter of Paraboloid)*sqrt(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1)
r = 1/(2*p)*sqrt(((6*LSA*p^2)/pi+1)^(2/3)-1)

What is Paraboloid?

In geometry, a Paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plane section of a paraboloid by a plane parallel to the axis of symmetry is a parabola. The paraboloid is hyperbolic if every other plane section is either a hyperbola, or two crossing lines (in the case of a section by a tangent plane). The paraboloid is elliptic if every other nonempty plane section is either an ellipse, or a single point (in the case of a section by a tangent plane). A paraboloid is either elliptic or hyperbolic.

How to Calculate Radius of Paraboloid given Lateral Surface Area?

Radius of Paraboloid given Lateral Surface Area calculator uses Radius of Paraboloid = 1/(2*Shape Parameter of Paraboloid)*sqrt(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1) to calculate the Radius of Paraboloid, The Radius of Paraboloid given Lateral Surface Area formula is defined as the length of the straight line from the center to any point on the circumference of the circular face of the Paraboloid, calculated using lateral surface area. Radius of Paraboloid is denoted by r symbol.

How to calculate Radius of Paraboloid given Lateral Surface Area using this online calculator? To use this online calculator for Radius of Paraboloid given Lateral Surface Area, enter Shape Parameter of Paraboloid (p) & Lateral Surface Area of Paraboloid (LSA) and hit the calculate button. Here is how the Radius of Paraboloid given Lateral Surface Area calculation can be explained with given input values -> 4.998416 = 1/(2*2)*sqrt(((6*1050*2^2)/pi+1)^(2/3)-1).

FAQ

What is Radius of Paraboloid given Lateral Surface Area?

The Radius of Paraboloid given Lateral Surface Area formula is defined as the length of the straight line from the center to any point on the circumference of the circular face of the Paraboloid, calculated using lateral surface area and is represented as r = 1/(2*p)*sqrt(((6*LSA*p^2)/pi+1)^(2/3)-1) or Radius of Paraboloid = 1/(2*Shape Parameter of Paraboloid)*sqrt(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1). Shape Parameter of Paraboloid is the total length of the boundary or outer edge of Paraboloid & Lateral Surface Area of Paraboloid is the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid.

How to calculate Radius of Paraboloid given Lateral Surface Area?

The Radius of Paraboloid given Lateral Surface Area formula is defined as the length of the straight line from the center to any point on the circumference of the circular face of the Paraboloid, calculated using lateral surface area is calculated using Radius of Paraboloid = 1/(2*Shape Parameter of Paraboloid)*sqrt(((6*Lateral Surface Area of Paraboloid*Shape Parameter of Paraboloid^2)/pi+1)^(2/3)-1). To calculate Radius of Paraboloid given Lateral Surface Area, you need Shape Parameter of Paraboloid (p) & Lateral Surface Area of Paraboloid (LSA). With our tool, you need to enter the respective value for Shape Parameter of Paraboloid & Lateral Surface Area of Paraboloid 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 Radius of Paraboloid?

In this formula, Radius of Paraboloid uses Shape Parameter of Paraboloid & Lateral Surface Area of Paraboloid. We can use 4 other way(s) to calculate the same, which is/are as follows -

Radius of Paraboloid = sqrt((Total Surface Area of Paraboloid-Lateral Surface Area of Paraboloid)/pi)
Radius of Paraboloid = sqrt((2*Volume of Paraboloid)/(pi*Height of Paraboloid))
Radius of Paraboloid = sqrt(Lateral Surface Area of Paraboloid/((1/2*Surface to Volume Ratio of Paraboloid*pi*Height of Paraboloid)-pi))
Radius of Paraboloid = sqrt(Height of Paraboloid/Shape Parameter of Paraboloid)

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