Question

A sector with a central angle measure of 200 degrees has a radius of 9 cm. What is the area of the sector?

Answer 1

`\boxed{Area\ of\ sector = 141.4\ cm^2}`

Explanation:

Radius = r = 9 cm

Angle = θ = 200° = 3.5 radians

Now,

`Area \ of \ sector = (1)/(2) r^2 \theta`

Area = 1/2 (9)²(3.5)

Area = 1/2 (81)(3.5)

Area = 282.7 / 2

Area of sector = 141.4 cm²

Answer 2

45 pi cm^2 or 141.3 cm^2

Explanation:

First find the area of the circle

A = pi r^2

A = pi (9)^2

A = 81 pi

A circle has 360 degrees

The shaded part has 200

The fraction that is shaded is

200/360 =5/9

Multiply by the total area

5/9 * 81 pi

45 pi

Using 3.14 for pi

141.3

45 pi cm^2 or 141.3 cm^2