Question

To the nearest square centimeter, what is the area of the shaded sector in the circle shown below?

Answer 1

the answer is the option B

`138\ cm^(2)`

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

we have

`r=12\ cm`

substitute

`A=\pi (12)^(2)=144\pi\ cm^(2)`

Remember that

`360\°` subtends the complete circle of area
`144\pi\ cm^(2)`

so

by proportion

find the area of the shaded sector for a central angle of
`110\°`

`(144\pi )/(360) (cm^(2))/(degrees) =(x)/(110) (cm^(2))/(degrees) \\ \\x=144\pi *110/360\\ \\x= 138.23\ cm^(2)`

Round to the nearest square centimeter

`x= 138\ cm^(2)`

Answer 2

area of circle = pir^2

r = 12

3.14 x 12^2 = 452.16 sq cm

110/360 = 0.3055

0.3055 x 452.16 = 138.16 round off to 138 cm^2

B is the answer