Question

Help me solve the area with steps

Answer 1

Answer:

$\frac{605}{6}\pi \ cm^2$  or $316.62\ cm^2$

Step-by-step explanation:

step 1

Find the area of complete circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=11\ cm$

substitute

$A=\pi (11)^{2}$

$A=121\pi\ cm^2$

step 2

Find the area of the sector

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

so

using proportion

Find out the area of the region by a central angle of 300 degrees

$\frac{121\pi}{360^o}=\frac{x}{300^o}\\\\x=121\pi (\frac{300^o}{360^o})\\\\x=\frac{36,300}{360}\pi\ cm^2$

simplify

$x=\frac{605}{6}\pi \ cm^2$ ----> exact value

Find the approximate value

assume

$\pi =3.14$

$x=\frac{605}{6}(3.14)=316.62\ cm^2$