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Area of Circle given central angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
area = (Central Angle/(2*pi))*pi*Radius^2
A = (Anglecentral/(2*pi))*pi*r^2
This formula uses 1 Constants, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
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)
Radius - Radius is a radial line from the focus to any point of a curve. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Central Angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
Radius: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = (Anglecentral/(2*pi))*pi*r^2 --> (0.785398163397301/(2*pi))*pi*10^2
Evaluating ... ...
A = 39.269908169865
STEP 3: Convert Result to Output's Unit
39.269908169865 Square Meter --> No Conversion Required
FINAL ANSWER
39.269908169865 Square Meter <-- Area
(Calculation completed in 00.000 seconds)

7 Area of Circle Calculators

Area of segment of Circle given central angle
area = (Radius^2/2)*(((pi/pi)*Central Angle)-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 Circle given central angle Formula

area = (Central Angle/(2*pi))*pi*Radius^2
A = (Anglecentral/(2*pi))*pi*r^2

What is an intercept arc?

An intercepted arc can therefore be defined as an arc formed when one or two different chords or line segments cut across a circle and meet at a common point called a vertex. It is important to note that the lines or the chords can either meet in the middle of a circle, on the other side of a circle or outside a circle.

How to Calculate Area of Circle given central angle?

Area of Circle given central angle calculator uses area = (Central Angle/(2*pi))*pi*Radius^2 to calculate the Area, The Area of circle given central angle formula is defined as formed by the two radii and the arc formed by these radii on the circumference, where r= radius. Area and is denoted by A symbol.

How to calculate Area of Circle given central angle using this online calculator? To use this online calculator for Area of Circle given central angle, enter Central Angle (Anglecentral) & Radius (r) and hit the calculate button. Here is how the Area of Circle given central angle calculation can be explained with given input values -> 39.26991 = (0.785398163397301/(2*pi))*pi*10^2.

FAQ

What is Area of Circle given central angle?
The Area of circle given central angle formula is defined as formed by the two radii and the arc formed by these radii on the circumference, where r= radius and is represented as A = (Anglecentral/(2*pi))*pi*r^2 or area = (Central Angle/(2*pi))*pi*Radius^2. 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 & Radius is a radial line from the focus to any point of a curve.
How to calculate Area of Circle given central angle?
The Area of circle given central angle formula is defined as formed by the two radii and the arc formed by these radii on the circumference, where r= radius is calculated using area = (Central Angle/(2*pi))*pi*Radius^2. To calculate Area of Circle given central angle, you need Central Angle (Anglecentral) & Radius (r). With our tool, you need to enter the respective value for Central Angle & Radius 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 Central Angle & Radius. We can use 7 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 = (Radius^2/2)*(((pi/pi)*Central Angle)-Central Angle)
  • area = (Central Angle/(2*pi))*pi*Radius^2
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