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Total Surface Area of Paraboloid given Volume Formula

GoTotal Surface Area of Paraboloid given Lateral Surface Area Formula

GoTotal Surface Area of Paraboloid given Surface to Volume Ratio Formula

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Total Surface Area of Paraboloid is the total quantity of two dimensional space enclosed on the entire surface of the Paraboloid. Check FAQs

TSA = (\frac{π \cdot \sqrt{\frac{2 \cdot V}{π \cdot h}}}{6 \cdot h^{2}} \cdot ({(\frac{2 \cdot V}{π \cdot h} + {(2 \cdot h)}^{2})}^{\frac{3}{2}} - \frac{2 \cdot V}{{(π \cdot h)}^{\frac{3}{2}}})) + (π \cdot r^{2})

TSA - Total Surface Area of Paraboloid?V - Volume of Paraboloid?h - Height of Paraboloid?r - Radius of Paraboloid?π - Archimedes' constant?

Total Surface Area of Paraboloid given Volume Example

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Here is how the Total Surface Area of Paraboloid given Volume equation looks like with Values.

Here is how the Total Surface Area of Paraboloid given Volume equation looks like with Units.

Here is how the Total Surface Area of Paraboloid given Volume equation looks like.

1139.4645 = (\frac{3.1416 \cdot \sqrt{\frac{2 \cdot 2000}{3.1416 \cdot 50}}}{6 \cdot 50^{2}} \cdot ({(\frac{2 \cdot 2000}{3.1416 \cdot 50} + {(2 \cdot 50)}^{2})}^{\frac{3}{2}} - \frac{2 \cdot 2000}{{(3.1416 \cdot 50)}^{\frac{3}{2}}})) + (3.1416 \cdot 5^{2})

1139.4645m² = (\frac{3.1416 \cdot \sqrt{\frac{2 \cdot 2000m³}{3.1416 \cdot 50m}}}{6 \cdot {50m}^{2}} \cdot ({(\frac{2 \cdot 2000m³}{3.1416 \cdot 50m} + {(2 \cdot 50m)}^{2})}^{\frac{3}{2}} - \frac{2 \cdot 2000m³}{{(3.1416 \cdot 50m)}^{\frac{3}{2}}})) + (3.1416 \cdot {5m}^{2})

1139.4645 = (\frac{3.1416 \cdot \sqrt{\frac{2 \cdot 2000}{3.1416 \cdot 50}}}{6 \cdot 50^{2}} \cdot ({(\frac{2 \cdot 2000}{3.1416 \cdot 50} + {(2 \cdot 50)}^{2})}^{\frac{3}{2}} - \frac{2 \cdot 2000}{{(3.1416 \cdot 50)}^{\frac{3}{2}}})) + (3.1416 \cdot 5^{2})

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Total Surface Area of Paraboloid given Volume Solution

Follow our step by step solution on how to calculate Total Surface Area of Paraboloid given Volume?

FIRST Step Consider the formula

TSA = (\frac{π \cdot \sqrt{\frac{2 \cdot V}{π \cdot h}}}{6 \cdot h^{2}} \cdot ({(\frac{2 \cdot V}{π \cdot h} + {(2 \cdot h)}^{2})}^{\frac{3}{2}} - \frac{2 \cdot V}{{(π \cdot h)}^{\frac{3}{2}}})) + (π \cdot r^{2})

Next Step Substitute values of Variables

∴

TSA = (\frac{π \cdot \sqrt{\frac{2 \cdot 2000m³}{π \cdot 50m}}}{6 \cdot {50m}^{2}} \cdot ({(\frac{2 \cdot 2000m³}{π \cdot 50m} + {(2 \cdot 50m)}^{2})}^{\frac{3}{2}} - \frac{2 \cdot 2000m³}{{(π \cdot 50m)}^{\frac{3}{2}}})) + (π \cdot {5m}^{2})

Next Step Substitute values of Constants

∴

TSA = (\frac{3.1416 \cdot \sqrt{\frac{2 \cdot 2000m³}{3.1416 \cdot 50m}}}{6 \cdot {50m}^{2}} \cdot ({(\frac{2 \cdot 2000m³}{3.1416 \cdot 50m} + {(2 \cdot 50m)}^{2})}^{\frac{3}{2}} - \frac{2 \cdot 2000m³}{{(3.1416 \cdot 50m)}^{\frac{3}{2}}})) + (3.1416 \cdot {5m}^{2})

Next Step Prepare to Evaluate

∴

TSA = (\frac{3.1416 \cdot \sqrt{\frac{2 \cdot 2000}{3.1416 \cdot 50}}}{6 \cdot 50^{2}} \cdot ({(\frac{2 \cdot 2000}{3.1416 \cdot 50} + {(2 \cdot 50)}^{2})}^{\frac{3}{2}} - \frac{2 \cdot 2000}{{(3.1416 \cdot 50)}^{\frac{3}{2}}})) + (3.1416 \cdot 5^{2})

Next Step Evaluate

∴

TSA = 1139.46452930883m²

LAST Step Rounding Answer

∴

TSA = 1139.4645m²

Total Surface Area of Paraboloid given Volume Formula Elements

Variables

Constants

Functions

Total Surface Area of Paraboloid

Total Surface Area of Paraboloid is the total quantity of two dimensional space enclosed on the entire surface of the Paraboloid.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Paraboloid

Volume of Paraboloid

Volume of Paraboloid is the amount of three dimensional space occupied by the Paraboloid.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Paraboloid

Height of Paraboloid

Height of Paraboloid is the vertical distance from the centre of the circular face to the local extreme point of the Paraboloid.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Paraboloid

Radius of 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.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Paraboloid

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Total Surface Area of Paraboloid

Go Total Surface Area of Paraboloid given Lateral Surface Area

TSA = LSA + π \cdot r^{2}

Go Total Surface Area of Paraboloid given Surface to Volume Ratio

TSA = \frac{1}{2} \cdot π \cdot r^{2} \cdot h \cdot R A/V

Go Total Surface Area of Paraboloid

TSA = (\frac{π \cdot r}{6 \cdot h^{2}} \cdot ({(r^{2} + 4 \cdot h^{2})}^{\frac{3}{2}} - r^{3})) + π \cdot r^{2}

Go Total Surface Area of Paraboloid given Radius

TSA = \frac{π}{6 \cdot p^{2}} \cdot ({(1 + 4 \cdot p^{2} \cdot r^{2})}^{\frac{3}{2}} - 1) + (π \cdot r^{2})

How to Evaluate Total Surface Area of Paraboloid given Volume?

Total Surface Area of Paraboloid given Volume evaluator 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 evaluate 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 evaluate Total Surface Area of Paraboloid given Volume using this online evaluator? To use this online evaluator 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.

FAQs on Total Surface Area of Paraboloid given Volume

What is the formula to find Total Surface Area of Paraboloid given Volume?

The formula of Total Surface Area of Paraboloid given Volume is expressed as 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). Here is an example- 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).

How to calculate Total Surface Area of Paraboloid given Volume?

With Volume of Paraboloid (V), Height of Paraboloid (h) & Radius of Paraboloid (r) we can find Total Surface Area of Paraboloid given Volume using the formula - 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). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Paraboloid?

Here are the different ways to Calculate Total Surface Area of Paraboloid-

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

Can the Total Surface Area of Paraboloid given Volume be negative?

No, the Total Surface Area of Paraboloid given Volume, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Paraboloid given Volume?

Total Surface Area of Paraboloid given Volume is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Paraboloid given Volume can be measured.

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Total Surface Area of Paraboloid given Volume Formula

​GoTotal Surface Area of Paraboloid given Lateral Surface Area Formula

​GoTotal Surface Area of Paraboloid given Surface to Volume Ratio Formula

Total Surface Area of Paraboloid given Volume Example

Total Surface Area of Paraboloid given Volume Solution

Total Surface Area of Paraboloid given Volume Formula Elements

Other Formulas to find Total Surface Area of Paraboloid

How to Evaluate Total Surface Area of Paraboloid given Volume?

FAQs on Total Surface Area of Paraboloid given Volume

Variable Name

GoTotal Surface Area of Paraboloid given Lateral Surface Area Formula

GoTotal Surface Area of Paraboloid given Surface to Volume Ratio Formula