Lateral Surface Area of Paraboloid Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
LSA = (pi*r)/(6*h^2)*((r^2+4*h^2)^(3/2)-r^3)
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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.
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.
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
Radius of Paraboloid: 5 Meter --> 5 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*r)/(6*h^2)*((r^2+4*h^2)^(3/2)-r^3) --> (pi*5)/(6*50^2)*((5^2+4*50^2)^(3/2)-5^3)
Evaluating ... ...
LSA = 1050.99609566725
STEP 3: Convert Result to Output's Unit
1050.99609566725 Square Meter --> No Conversion Required
FINAL ANSWER
1050.99609566725 1050.996 Square Meter <-- Lateral Surface Area of Paraboloid
(Calculation completed in 00.004 seconds)

Credits

Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
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Indian Institute of Information Technology (IIIT), Bhopal
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6 Lateral Surface Area of Paraboloid Calculators

Lateral Surface Area of Paraboloid given Volume
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
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
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 Radius
Go Lateral Surface Area of Paraboloid = pi/(6*Shape Parameter of Paraboloid^2)*((1+4*Shape Parameter of Paraboloid^2*Radius of Paraboloid^2)^(3/2)-1)
Lateral Surface Area of Paraboloid given Height
Go Lateral Surface Area of Paraboloid = pi/(6*Shape Parameter of Paraboloid^2)*((1+4*Height of Paraboloid*Shape Parameter of Paraboloid)^(3/2)-1)
Lateral Surface Area of Paraboloid given Total Surface Area
Go Lateral Surface Area of Paraboloid = Total Surface Area of Paraboloid-pi*Radius of Paraboloid^2

7 Surface Area of Paraboloid Calculators

Total Surface Area of Paraboloid
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 Height
Go Total Surface Area of Paraboloid = pi/(6*Shape Parameter of Paraboloid^2)*((1+4*Shape Parameter of Paraboloid*Height of Paraboloid)^(3/2)-1)+(pi*Height of Paraboloid)/Shape Parameter of Paraboloid
Total Surface Area of Paraboloid given Radius
Go Total Surface Area of Paraboloid = pi/(6*Shape Parameter of Paraboloid^2)*((1+4*Shape Parameter of Paraboloid^2*Radius of Paraboloid^2)^(3/2)-1)+(pi*Radius of Paraboloid^2)
Lateral Surface Area of Paraboloid
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 Height
Go Lateral Surface Area of Paraboloid = pi/(6*Shape Parameter of Paraboloid^2)*((1+4*Height of Paraboloid*Shape Parameter of Paraboloid)^(3/2)-1)
Lateral Surface Area of Paraboloid given Total Surface Area
Go Lateral Surface Area of Paraboloid = Total Surface Area of Paraboloid-pi*Radius of Paraboloid^2
Total Surface Area of Paraboloid given Lateral Surface Area
Go Total Surface Area of Paraboloid = Lateral Surface Area of Paraboloid+pi*Radius of Paraboloid^2

Lateral Surface Area of Paraboloid Formula

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)
LSA = (pi*r)/(6*h^2)*((r^2+4*h^2)^(3/2)-r^3)

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?

Lateral Surface Area of Paraboloid calculator uses 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) to calculate the Lateral Surface Area of Paraboloid, Lateral Surface Area of Paraboloid formula is defined as the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid. Lateral Surface Area of Paraboloid is denoted by LSA symbol.

How to calculate Lateral Surface Area of Paraboloid using this online calculator? To use this online calculator for Lateral Surface Area of Paraboloid, enter Radius of Paraboloid (r) & Height of Paraboloid (h) and hit the calculate button. Here is how the Lateral Surface Area of Paraboloid calculation can be explained with given input values -> 1050.996 = (pi*5)/(6*50^2)*((5^2+4*50^2)^(3/2)-5^3).

FAQ

What is Lateral Surface Area of Paraboloid?
Lateral Surface Area of Paraboloid formula is defined as the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid and is represented as LSA = (pi*r)/(6*h^2)*((r^2+4*h^2)^(3/2)-r^3) or 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). 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 & 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?
Lateral Surface Area of Paraboloid formula is defined as the total quantity of two dimensional plane enclosed on the lateral curved surface of Paraboloid is calculated using 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). To calculate Lateral Surface Area of Paraboloid, you need Radius of Paraboloid (r) & Height of Paraboloid (h). With our tool, you need to enter the respective value for Radius 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 Radius of Paraboloid & Height of Paraboloid. We can use 7 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*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 = 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 = pi/(6*Shape Parameter of Paraboloid^2)*((1+4*Shape Parameter of Paraboloid^2*Radius of Paraboloid^2)^(3/2)-1)
  • Lateral Surface Area of Paraboloid = pi/(6*Shape Parameter of Paraboloid^2)*((1+4*Height of Paraboloid*Shape Parameter of Paraboloid)^(3/2)-1)
  • Lateral Surface Area of Paraboloid = pi/(6*Shape Parameter of Paraboloid^2)*((1+4*Height of Paraboloid*Shape Parameter of Paraboloid)^(3/2)-1)
  • Lateral Surface Area of Paraboloid = Total Surface Area of Paraboloid-pi*Radius of Paraboloid^2
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