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Area of segment of Circle given central angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area = (1/2)*(Radius^2)*(Central Angle-sin(Central Angle))
A = (1/2)*(r^2)*(central-sin(central))
This formula uses 1 Functions, 2 Variables
Functions Used
sin - Trigonometric sine function, sin(Angle)
Variables Used
Radius - Radius is a radial line from the focus to any point of a curve. (Measured in Meter)
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. (Measured in Degree)
STEP 1: Convert Input(s) to Base Unit
Radius: 10 Meter --> 10 Meter No Conversion Required
Central Angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = (1/2)*(r^2)*(∠central-sin(∠central)) --> (1/2)*(10^2)*(0.785398163397301-sin(0.785398163397301))
Evaluating ... ...
A = 3.91456911054288
STEP 3: Convert Result to Output's Unit
3.91456911054288 Square Meter --> No Conversion Required
FINAL ANSWER
3.91456911054288 Square Meter <-- Area
(Calculation completed in 00.000 seconds)

7 Area of Circle Calculators

Area of segment of Circle given central angle
Area = (1/2)*(Radius^2)*(Central Angle-sin(Central Angle)) Go
Area of Circle given central angle
Area = (Central Angle/(2*pi))*pi*Radius^2 Go
Area of Circle given area of sector
Area = Area of Sector*(360/Central Angle) Go
Area of Circle given circumference
Area = ((Circumference)^2)/(4*pi) Go
Area of Circle given diameter
Area = (pi/4)*Diameter^2 Go
Area of Circle given radius
Area = pi*Radius^2 Go
Area of Circle given area of quadrant
Area = 4*Area Go

Area of segment of Circle given central angle Formula

Area = (1/2)*(Radius^2)*(Central Angle-sin(Central Angle))
A = (1/2)*(r^2)*(central-sin(central))

What is Segment of a Circle?

A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord’s endpoints. In other words, a circular segment is a region of a circle which is created by breaking apart from the rest of the circle through a secant or a chord.

How to Calculate Area of segment of Circle given central angle?

Area of segment of Circle given central angle calculator uses Area = (1/2)*(Radius^2)*(Central Angle-sin(Central Angle)) to calculate the Area, Area of segment of circle given central angle formula is defined as found by calculating the area of the whole pie-shaped sector and subtracting the area of the isosceles triangle. Area is denoted by A symbol.

How to calculate Area of segment of Circle given central angle using this online calculator? To use this online calculator for Area of segment of Circle given central angle, enter Radius (r) & Central Angle (∠central) and hit the calculate button. Here is how the Area of segment of Circle given central angle calculation can be explained with given input values -> 3.914569 = (1/2)*(10^2)*(0.785398163397301-sin(0.785398163397301)).

FAQ

What is Area of segment of Circle given central angle?
Area of segment of circle given central angle formula is defined as found by calculating the area of the whole pie-shaped sector and subtracting the area of the isosceles triangle and is represented as A = (1/2)*(r^2)*(central-sin(central)) or Area = (1/2)*(Radius^2)*(Central Angle-sin(Central Angle)). Radius is a radial line from the focus to any point of a curve & 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.
How to calculate Area of segment of Circle given central angle?
Area of segment of circle given central angle formula is defined as found by calculating the area of the whole pie-shaped sector and subtracting the area of the isosceles triangle is calculated using Area = (1/2)*(Radius^2)*(Central Angle-sin(Central Angle)). To calculate Area of segment of Circle given central angle, you need Radius (r) & Central Angle (∠central). With our tool, you need to enter the respective value for Radius & Central Angle 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 Area?
In this formula, Area uses Radius & Central Angle. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Area = pi*Radius^2
  • Area = (pi/4)*Diameter^2
  • Area = ((Circumference)^2)/(4*pi)
  • Area = Area of Sector*(360/Central Angle)
  • Area = 4*Area
  • Area = (Central Angle/(2*pi))*pi*Radius^2
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