Question

(25 points to correct answer)

Find the area of sector GHJ given that θ=65°. Use 3.14 for π and round to the nearest tenth. Show your work and do not forget to include units in your final answer.

Answer 1

The area of a sector GHJ is
`36.3\ cm^(2)`

Explanation:

step 1

we know that

The area of a circle is equal to

`A=\pi r^(2)`

we have

`r=8\ cm`

substitute

`A=\pi (8)^(2)`

`A=64\pi\ cm^(2)`

step 2

Remember that the area of a complete circle subtends a central angle of 360 degrees

so

by proportion find the area of a sector by a central angle of 65 degrees

`(64\pi)/(360)=(x)/(65)\\ \\x=64\pi (65)/360`

Use
`\pi =3.14`

`x=64(3.14)(65)/360=36.3\ cm^(2)`