Question

In this circle the area of the sector COD is 50.24

Answer 1

To find the angle of a sector in a circle, you can use the formula (angle/360) x πr². Rearrange the formula to solve for the angle when given the area of the sector.

Step-by-step explanation:

The area of a sector in a circle can be found using the formula:

Area of sector = (angle/360) x πr²

Given that the area of sector COD is 50.24, we can set up the equation as follows:

50.24 = (angle/360) x πr²

To solve for the angle, we can rearrange the equation:

angle = (50.24 x 360) / (πr²)

Once we know the angle, we can find other properties of the sector, such as arc length and radius.

Answer 2

The area of the sector is equal to half of the square of the radius times the opening of the sector (theta). Basing on the figure, the angle of sector COD is 90 degrees. So,

Area of sector = 50.24 = (1/2) * (r^2) (theta)

The theta should be expressed in radians. So, we convert 90 degrees to radians:

90 degrees (pi rad/180 degrees) = pi/2

Thus,
50.42 = (1/2) * (r^2) * (pi/2)
r^2 = 64.2
r = 8.01 units

Thus, the radius of the sector is 8.1 units.