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Total Surface Area of Paraboloid Formula

GoTotal Surface Area of Paraboloid given Height Formula

GoTotal Surface Area of Paraboloid given Lateral Surface Area 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 r}{6 \cdot h^{2}} \cdot ({(r^{2} + 4 \cdot h^{2})}^{\frac{3}{2}} - r^{3})) + π \cdot r^{2}

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

Total Surface Area of Paraboloid Example

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

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

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

1129.5359 = (\frac{3.1416 \cdot 5}{6 \cdot 50^{2}} \cdot ({(5^{2} + 4 \cdot 50^{2})}^{\frac{3}{2}} - 5^{3})) + 3.1416 \cdot 5^{2}

1129.5359m² = (\frac{3.1416 \cdot 5m}{6 \cdot {50m}^{2}} \cdot ({({5m}^{2} + 4 \cdot {50m}^{2})}^{\frac{3}{2}} - {5m}^{3})) + 3.1416 \cdot {5m}^{2}

1129.5359 = (\frac{3.1416 \cdot 5}{6 \cdot 50^{2}} \cdot ({(5^{2} + 4 \cdot 50^{2})}^{\frac{3}{2}} - 5^{3})) + 3.1416 \cdot 5^{2}

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Total Surface Area of Paraboloid Solution

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

FIRST Step Consider the formula

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}

Next Step Substitute values of Variables

∴

TSA = (\frac{π \cdot 5m}{6 \cdot {50m}^{2}} \cdot ({({5m}^{2} + 4 \cdot {50m}^{2})}^{\frac{3}{2}} - {5m}^{3})) + π \cdot {5m}^{2}

Next Step Substitute values of Constants

∴

TSA = (\frac{3.1416 \cdot 5m}{6 \cdot {50m}^{2}} \cdot ({({5m}^{2} + 4 \cdot {50m}^{2})}^{\frac{3}{2}} - {5m}^{3})) + 3.1416 \cdot {5m}^{2}

Next Step Prepare to Evaluate

∴

TSA = (\frac{3.1416 \cdot 5}{6 \cdot 50^{2}} \cdot ({(5^{2} + 4 \cdot 50^{2})}^{\frac{3}{2}} - 5^{3})) + 3.1416 \cdot 5^{2}

Next Step Evaluate

∴

TSA = 1129.53591200699m²

LAST Step Rounding Answer

∴

TSA = 1129.5359m²

Total Surface Area of Paraboloid Formula Elements

Variables

Constants

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

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

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

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

Other Formulas to find Total Surface Area of Paraboloid

Go Total Surface Area of Paraboloid given Height

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

Go Total Surface Area of Paraboloid given Lateral Surface Area

TSA = LSA + 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})

Other formulas in Total Surface Area of Paraboloid category

Go Lateral Surface Area of Paraboloid

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

Go Lateral Surface Area of Paraboloid given Height

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

Go Lateral Surface Area of Paraboloid given Total Surface Area

LSA = TSA - π \cdot r^{2}

How to Evaluate Total Surface Area of Paraboloid?

Total Surface Area of Paraboloid evaluator uses 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 to evaluate the Total Surface Area of Paraboloid, The Total Surface Area of Paraboloid formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Paraboloid. Total Surface Area of Paraboloid is denoted by TSA symbol.

How to evaluate Total Surface Area of Paraboloid using this online evaluator? To use this online evaluator for Total Surface Area of Paraboloid, enter Radius of Paraboloid (r) & Height of Paraboloid (h) and hit the calculate button.

FAQs on Total Surface Area of Paraboloid

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

The formula of Total Surface Area of Paraboloid is expressed as 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. Here is an example- 1129.536 = ((pi*5)/(6*50^2)*((5^2+4*50^2)^(3/2)-5^3))+pi*5^2.

How to calculate Total Surface Area of Paraboloid?

With Radius of Paraboloid (r) & Height of Paraboloid (h) we can find Total Surface Area of Paraboloid using the formula - 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. This formula also uses Archimedes' constant .

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=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=Lateral Surface Area of Paraboloid+pi*Radius of Paraboloid^2
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)

Can the Total Surface Area of Paraboloid be negative?

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

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

Total Surface Area of Paraboloid 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 can be measured.

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Total Surface Area of Paraboloid Formula

​GoTotal Surface Area of Paraboloid given Height Formula

​GoTotal Surface Area of Paraboloid given Lateral Surface Area Formula

Total Surface Area of Paraboloid Example

Total Surface Area of Paraboloid Solution

Total Surface Area of Paraboloid Formula Elements

Other Formulas to find Total Surface Area of Paraboloid

Other formulas in Total Surface Area of Paraboloid category

How to Evaluate Total Surface Area of Paraboloid?

FAQs on Total Surface Area of Paraboloid

Variable Name

GoTotal Surface Area of Paraboloid given Height Formula

GoTotal Surface Area of Paraboloid given Lateral Surface Area Formula