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Proportionate Area given Central Angle Formula

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Proportionate Area is ratio of area when water is partially full to area when water is totally full. Check FAQs

P a = ((\frac{∠ central}{360 \cdot \frac{π}{180}}) - (\frac{\sin (∠ central)}{2 \cdot π}))

P_a - Proportionate Area?∠_central - Central Angle?π - Archimedes' constant?

Proportionate Area given Central Angle Example

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Here is how the Proportionate Area given Central Angle equation looks like with Values.

Here is how the Proportionate Area given Central Angle equation looks like with Units.

Here is how the Proportionate Area given Central Angle equation looks like.

0.1955 = ((\frac{120}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (120)}{2 \cdot 3.1416}))

0.1955 = ((\frac{120°}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (120°)}{2 \cdot 3.1416}))

0.1955 = ((\frac{120}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (120)}{2 \cdot 3.1416}))

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Proportionate Area given Central Angle Solution

Follow our step by step solution on how to calculate Proportionate Area given Central Angle?

FIRST Step Consider the formula

P a = ((\frac{∠ central}{360 \cdot \frac{π}{180}}) - (\frac{\sin (∠ central)}{2 \cdot π}))

Next Step Substitute values of Variables

∴

P a = ((\frac{120°}{360 \cdot \frac{π}{180}}) - (\frac{\sin (120°)}{2 \cdot π}))

Next Step Substitute values of Constants

∴

P a = ((\frac{120°}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (120°)}{2 \cdot 3.1416}))

Next Step Convert Units

∴

P a = ((\frac{2.0944rad}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (2.0944rad)}{2 \cdot 3.1416}))

Next Step Prepare to Evaluate

∴

P a = ((\frac{2.0944}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (2.0944)}{2 \cdot 3.1416}))

Next Step Evaluate

∴

P a = 0.195501109477791

LAST Step Rounding Answer

∴

P a = 0.1955

Proportionate Area given Central Angle Formula Elements

Variables

Constants

Functions

Proportionate Area

Proportionate Area is ratio of area when water is partially full to area when water is totally full.

Symbol: P_a

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Proportionate Area

Central Angle

A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B.

Symbol: ∠_central

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Formulas to find Central Angle

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other Formulas to find Proportionate Area

Go Proportionate Area given Area of Cross-section

P a = \frac{a}{A}

Other formulas in Proportionate Area category

Go Area of Cross-section given Proportionate Area

A = \frac{a}{P a}

How to Evaluate Proportionate Area given Central Angle?

Proportionate Area given Central Angle evaluator uses Proportionate Area = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi))) to evaluate the Proportionate Area, The Proportionate Area given Central Angle is defined as the cross-sectional area of flow when a pipe is not completely full to when it is entirely filled. Proportionate Area is denoted by P_a symbol.

How to evaluate Proportionate Area given Central Angle using this online evaluator? To use this online evaluator for Proportionate Area given Central Angle, enter Central Angle (∠_central) and hit the calculate button.

FAQs on Proportionate Area given Central Angle

What is the formula to find Proportionate Area given Central Angle?

The formula of Proportionate Area given Central Angle is expressed as Proportionate Area = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi))). Here is an example- 0.01246 = ((central_angle/(360*pi/180))-(sin(central_angle)/(2*pi))).

How to calculate Proportionate Area given Central Angle?

With Central Angle (∠_central) we can find Proportionate Area given Central Angle using the formula - Proportionate Area = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi))). This formula also uses Archimedes' constant and Sine function(s).

What are the other ways to Calculate Proportionate Area?

Here are the different ways to Calculate Proportionate Area-

Proportionate Area=Area of Partially Full Sewers/Area of Running Full Sewers

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