Question

Help me solve the area with steps

Answer 1

`(605)/(6)\pi \ cm^2` or
`316.62\ cm^2`

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

`(121\pi)/(360^o)=(x)/(300^o)\\\\x=121\pi ((300^o)/(360^o))\\\\x=(36,300)/(360)\pi\ cm^2`

simplify

`x=(605)/(6)\pi \ cm^2` ----> exact value

Find the approximate value

assume

`\pi =3.14`

`x=(605)/(6)(3.14)=316.62\ cm^2`