XOY is a real sector of a circle center O of radius 3.5cm which subtends an angle of 144o at the center. Calculate, in term of ϖ, the area of the sector

Answer Details

To find the area of the sector, we first need to find the length of the arc XOY.

The formula for the length of an arc of a sector is given by:

length of arc = (angle/360) x 2 x ϖ x radius

Substituting the given values, we get:

length of arc = (144/360) x 2 x ϖ x 3.5

Simplifying this expression, we get:

length of arc = 1.4ϖ

So the length of arc XOY is 1.4ϖ cm.

To find the area of the sector, we use the formula:

area of sector = (angle/360) x ϖ x radius^2

Substituting the given values, we get:

area of sector = (144/360) x ϖ x 3.5^2

Simplifying this expression, we get:

area of sector = 4.9ϖ

Therefore, the area of the sector is 4.9ϖ cm².

So the correct option is 4.