Lateral Surface Area of Paraboloid given Volume Calculator

✖Volume of Paraboloid is the amount of three dimensional space occupied by the Paraboloid.ⓘ Volume of Paraboloid [V]			+10% -10%
✖Height of Paraboloid is the vertical distance from the centre of the circular face to the local extreme point of the Paraboloid.ⓘ Height of Paraboloid [h]			+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 given Volume [LSA]

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Lateral Surface Area of Paraboloid given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Lateral Surface Area of Paraboloid = (pi*sqrt((2*Volume of Paraboloid)/(pi*Height of Paraboloid)))/(6*Height of Paraboloid^2)*(((2*Volume of Paraboloid)/(pi*Height of Paraboloid)+4*Height of Paraboloid^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2))
LSA = (pi*sqrt((2*V)/(pi*h)))/(6*h^2)*(((2*V)/(pi*h)+4*h^2)^(3/2)-(2*V)/(pi*h)^(3/2))
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

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.
Volume of Paraboloid - (Measured in Cubic Meter) - Volume of Paraboloid is the amount of three dimensional space occupied by the Paraboloid.
Height of Paraboloid - (Measured in Meter) - Height of Paraboloid is the vertical distance from the centre of the circular face to the local extreme point of the Paraboloid.

STEP 1: Convert Input(s) to Base Unit

Volume of Paraboloid: 2000 Cubic Meter --> 2000 Cubic Meter No Conversion Required
Height of Paraboloid: 50 Meter --> 50 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

LSA = (pi*sqrt((2*V)/(pi*h)))/(6*h^2)*(((2*V)/(pi*h)+4*h^2)^(3/2)-(2*V)/(pi*h)^(3/2)) --> (pi*sqrt((2*2000)/(pi*50)))/(6*50^2)*(((2*2000)/(pi*50)+4*50^2)^(3/2)-(2*2000)/(pi*50)^(3/2))

Evaluating ... ...

LSA = 1060.92471296908

STEP 3: Convert Result to Output's Unit

1060.92471296908 Square Meter --> No Conversion Required

FINAL ANSWER

1060.92471296908 ≈ 1060.925 Square Meter <-- Lateral Surface Area of Paraboloid

(Calculation completed in 00.020 seconds)

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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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< Lateral Surface Area of Paraboloid Calculators

Lateral Surface Area of Paraboloid given Volume

LaTeX Go Lateral Surface Area of Paraboloid = (pi*sqrt((2*Volume of Paraboloid)/(pi*Height of Paraboloid)))/(6*Height of Paraboloid^2)*(((2*Volume of Paraboloid)/(pi*Height of Paraboloid)+4*Height of Paraboloid^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2))

Lateral Surface Area of Paraboloid

LaTeX Go Lateral Surface Area of Paraboloid = (pi*Radius of Paraboloid)/(6*Height of Paraboloid^2)*((Radius of Paraboloid^2+4*Height of Paraboloid^2)^(3/2)-Radius of Paraboloid^3)

Lateral Surface Area of Paraboloid given Surface to Volume Ratio

LaTeX Go Lateral Surface Area of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid*Surface to Volume Ratio of Paraboloid-pi*Radius of Paraboloid^2

Lateral Surface Area of Paraboloid given Total Surface Area

LaTeX Go Lateral Surface Area of Paraboloid = Total Surface Area of Paraboloid-pi*Radius of Paraboloid^2

Lateral Surface Area of Paraboloid given Volume Formula

LaTeX Go

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 Lateral Surface Area of Paraboloid given Volume?

Lateral Surface Area of Paraboloid given Volume calculator uses Lateral Surface Area of Paraboloid = (pi*sqrt((2*Volume of Paraboloid)/(pi*Height of Paraboloid)))/(6*Height of Paraboloid^2)*(((2*Volume of Paraboloid)/(pi*Height of Paraboloid)+4*Height of Paraboloid^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2)) to calculate the Lateral Surface Area of Paraboloid, The Lateral Surface Area of Paraboloid given Volume formula is defined as the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid, calculated using volume of Paraboloid. Lateral Surface Area of Paraboloid is denoted by LSA symbol.

How to calculate Lateral Surface Area of Paraboloid given Volume using this online calculator? To use this online calculator for Lateral Surface Area of Paraboloid given Volume, enter Volume of Paraboloid (V) & Height of Paraboloid (h) and hit the calculate button. Here is how the Lateral Surface Area of Paraboloid given Volume calculation can be explained with given input values -> 1060.925 = (pi*sqrt((2*2000)/(pi*50)))/(6*50^2)*(((2*2000)/(pi*50)+4*50^2)^(3/2)-(2*2000)/(pi*50)^(3/2)).

FAQ

What is Lateral Surface Area of Paraboloid given Volume?

The Lateral Surface Area of Paraboloid given Volume formula is defined as the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid, calculated using volume of Paraboloid and is represented as LSA = (pi*sqrt((2*V)/(pi*h)))/(6*h^2)*(((2*V)/(pi*h)+4*h^2)^(3/2)-(2*V)/(pi*h)^(3/2)) or Lateral Surface Area of Paraboloid = (pi*sqrt((2*Volume of Paraboloid)/(pi*Height of Paraboloid)))/(6*Height of Paraboloid^2)*(((2*Volume of Paraboloid)/(pi*Height of Paraboloid)+4*Height of Paraboloid^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2)). Volume of Paraboloid is the amount of three dimensional space occupied by the Paraboloid & Height of Paraboloid is the vertical distance from the centre of the circular face to the local extreme point of the Paraboloid.

How to calculate Lateral Surface Area of Paraboloid given Volume?

The Lateral Surface Area of Paraboloid given Volume formula is defined as the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid, calculated using volume of Paraboloid is calculated using Lateral Surface Area of Paraboloid = (pi*sqrt((2*Volume of Paraboloid)/(pi*Height of Paraboloid)))/(6*Height of Paraboloid^2)*(((2*Volume of Paraboloid)/(pi*Height of Paraboloid)+4*Height of Paraboloid^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2)). To calculate Lateral Surface Area of Paraboloid given Volume, you need Volume of Paraboloid (V) & Height of Paraboloid (h). With our tool, you need to enter the respective value for Volume of Paraboloid & Height 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 Lateral Surface Area of Paraboloid?

In this formula, Lateral Surface Area of Paraboloid uses Volume of Paraboloid & Height of Paraboloid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Lateral Surface Area of Paraboloid = Total Surface Area of Paraboloid-pi*Radius of Paraboloid^2
Lateral Surface Area of Paraboloid = (pi*Radius of Paraboloid)/(6*Height of Paraboloid^2)*((Radius of Paraboloid^2+4*Height of Paraboloid^2)^(3/2)-Radius of Paraboloid^3)
Lateral Surface Area of Paraboloid = 1/2*pi*Radius of Paraboloid^2*Height of Paraboloid*Surface to Volume Ratio of Paraboloid-pi*Radius of Paraboloid^2

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