If O is the centre of the circle and the area of sector OAPB is 5/18 of the area of circle . Find angle.
Since the area of the sector is 5/18 of the circle, the central angle must be 518 of 360° ,
which is ....
To find the angle of the sector OAPB, we first need to understand the relationship between the area of a sector and the angle it subtends at the center of the circle.
The area of a sector is proportional to the central angle that the sector subtends. In other words, if we double the angle, we double the area, and if we halve the angle, we halve the area.
Let's denote the angle subtended by the sector OAPB as θ. The area of the sector is given as 5/18 of the area of the entire circle.
Now, the area of a sector is calculated using the formula:
Area of sector = (θ/360) * π * r^2
where θ is the central angle and r is the radius of the circle.
Let's assume the radius of the circle is 'r', and the area of the entire circle is A.
Given that the area of the sector OAPB is 5/18 of the area of the circle, we can write the equation as:
(θ/360) * π * r^2 = (5/18) * A
To find the value of θ, we need more information. We either need the value of the radius 'r' or the area of the circle 'A'. Without this information, we cannot determine the specific value of the angle θ.