Question

if a circle of radius r made an angle at center is ,then what is the area of sector
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Answer 1

Answer:

hey mate here is ur answer

Step-by-step explanation:

If a circle of radius r made an angle at centre then the angle made by the arc to any point of the its circumference is the sector of the circle

hope it will help you

thankyu

Answer 2

One radian is equal to the angle formed when the arc opposite the angle is equal to the radius of the circle. So in the above diagram, the angle ø is equal to one radian since the arc AB is the same length as the radius of the circle.

Now, the circumference of the circle is 2 PI r, where r is the radius of the circle. So the circumference of a circle is 2 PI larger than its radius. This means that in any circle, there are 2 PI radians.

Therefore 360º = 2 PI radians.

Therefore 180º = PI radians.

So one radian = 180/ PI degrees and one degree = PI /180 radians.

Therefore to convert a certain number of degrees in to radians, multiply the number of degrees by PI /180 (for example, 90º = 90 × PI /180 radians = PI /2). To convert a certain number of radians into degrees, multiply the number of radians by 180/ PI .

Arc Length

The length of an arc of a circle is equal to ∅, where ∅ is the angle, in radians, subtended by the arc at the centre of the circle (see below diagram if you don’t understand). So in the below diagram, s = r∅ .

Radians

Area of Sector

The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle. So in the below diagram, the shaded area is equal to ½ r² ∅ .