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

Answer:

The area of a sector GHJ is $36.3\ cm^{2}$

Step-by-step 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

$\frac{64\pi}{360}=\frac{x}{65}\\ \\x=64\pi (65)/360$

Use $\pi =3.14$

$x=64(3.14)(65)/360=36.3\ cm^{2}$