What is the ratio of the area of sector AOB to the area of sector COD?
1/3,1/4,1/9,3/8
Since the area is 1/2 r^2 θ, the ratio is
1/2 r^2 m∠AOB
--------------- = (m∠AOB)/(m∠COD)
1/2 r^2 m∠COD
That is, since for a given circle, the area is directly proportional to the angle, the ratio of the areas is the same as the ratio of the angles.
I have no idea what that ratio is, but it must be one of the choices.
To find the ratio of the areas of the sectors, we need to know the angles of the sectors.
Let's assume that the central angle for sector AOB is θ1, and the central angle for sector COD is θ2.
The area of a sector can be calculated using the formula: Area = (θ/360) * π * r^2, where θ is the central angle and r is the radius of the circle.
To find the ratio of the areas of sector AOB to sector COD, we can calculate:
Area of sector AOB / Area of sector COD = [(θ1/360) * π * r^2] / [(θ2/360) * π * r^2]
Notice that the radius, r^2, is common to both sectors, so it cancels out.
We are given four options: 1/3, 1/4, 1/9, and 3/8. To determine which one is the answer, we need more information about the central angles θ1 and θ2.