Total 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%
✖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 [r]			+10% -10%

✖Total Surface Area of Paraboloid is the total quantity of two dimensional space enclosed on the entire surface of the Paraboloid.ⓘ Total Surface Area of Paraboloid given Volume [TSA]

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Total Surface Area of Paraboloid given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total 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)+(2*Height of Paraboloid)^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2)))+(pi*Radius of Paraboloid^2)
TSA = ((pi*sqrt((2*V)/(pi*h)))/(6*h^2)*(((2*V)/(pi*h)+(2*h)^2)^(3/2)-(2*V)/(pi*h)^(3/2)))+(pi*r^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

Total Surface Area of Paraboloid - (Measured in Square Meter) - Total Surface Area of Paraboloid is the total quantity of two dimensional space enclosed on the entire surface of the 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.
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.

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
Radius of Paraboloid: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = ((pi*sqrt((2*V)/(pi*h)))/(6*h^2)*(((2*V)/(pi*h)+(2*h)^2)^(3/2)-(2*V)/(pi*h)^(3/2)))+(pi*r^2) --> ((pi*sqrt((2*2000)/(pi*50)))/(6*50^2)*(((2*2000)/(pi*50)+(2*50)^2)^(3/2)-(2*2000)/(pi*50)^(3/2)))+(pi*5^2)

Evaluating ... ...

TSA = 1139.46452930883

STEP 3: Convert Result to Output's Unit

1139.46452930883 Square Meter --> No Conversion Required

FINAL ANSWER

1139.46452930883 ≈ 1139.465 Square Meter <-- Total Surface Area of Paraboloid

(Calculation completed in 00.004 seconds)

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Created by Divanshi Jain

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

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< Total Surface Area of Paraboloid Calculators

Total Surface Area of Paraboloid given Volume

LaTeX Go Total 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)+(2*Height of Paraboloid)^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2)))+(pi*Radius of Paraboloid^2)

Total Surface Area of Paraboloid

LaTeX Go Total 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))+pi*Radius of Paraboloid^2

Total Surface Area of Paraboloid given Surface to Volume Ratio

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

Total Surface Area of Paraboloid given Lateral Surface Area

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

Total 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 Total Surface Area of Paraboloid given Volume?

Total Surface Area of Paraboloid given Volume calculator uses Total 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)+(2*Height of Paraboloid)^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2)))+(pi*Radius of Paraboloid^2) to calculate the Total Surface Area of Paraboloid, The Total Surface Area of Paraboloid given Volume formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Paraboloid, calculated using volume of Paraboloid. Total Surface Area of Paraboloid is denoted by TSA symbol.

How to calculate Total Surface Area of Paraboloid given Volume using this online calculator? To use this online calculator for Total Surface Area of Paraboloid given Volume, enter Volume of Paraboloid (V), Height of Paraboloid (h) & Radius of Paraboloid (r) and hit the calculate button. Here is how the Total Surface Area of Paraboloid given Volume calculation can be explained with given input values -> 1139.465 = ((pi*sqrt((2*2000)/(pi*50)))/(6*50^2)*(((2*2000)/(pi*50)+(2*50)^2)^(3/2)-(2*2000)/(pi*50)^(3/2)))+(pi*5^2).

FAQ

What is Total Surface Area of Paraboloid given Volume?

The Total Surface Area of Paraboloid given Volume formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Paraboloid, calculated using volume of Paraboloid and is represented as TSA = ((pi*sqrt((2*V)/(pi*h)))/(6*h^2)*(((2*V)/(pi*h)+(2*h)^2)^(3/2)-(2*V)/(pi*h)^(3/2)))+(pi*r^2) or Total 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)+(2*Height of Paraboloid)^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2)))+(pi*Radius of Paraboloid^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 & 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.

How to calculate Total Surface Area of Paraboloid given Volume?

The Total Surface Area of Paraboloid given Volume formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Paraboloid, calculated using volume of Paraboloid is calculated using Total 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)+(2*Height of Paraboloid)^2)^(3/2)-(2*Volume of Paraboloid)/(pi*Height of Paraboloid)^(3/2)))+(pi*Radius of Paraboloid^2). To calculate Total Surface Area of Paraboloid given Volume, you need Volume of Paraboloid (V), Height of Paraboloid (h) & Radius of Paraboloid (r). With our tool, you need to enter the respective value for Volume of Paraboloid, Height of Paraboloid & Radius 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 Total Surface Area of Paraboloid?

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

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

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