Question

Can I get help with this problem?

Answer 1

area of sector:

`(theta)/(360) * \pi \: {r}^(2)`

`(165)/(360) * (22)/(7) ( {8}^(2) )`

`(11)/(24) * (1408)/(7)`

`(1936)/(21)`

`92.19 \: {in}^(2)`

Answer 2

the area of the sector can be rounded to
`92.2\,\,in^2`

Explanation:

Use the fraction of the area of the circle associated with the red sector. Use a proportion to find the appropriate fraction knowing that a full circle
`(360^o)` corresponds to the area:

`Area=\pi\,R^2=\pi\, (8\,in)^2= 64\, \pi\,\,in^2`

then the proportion goes like:

`(64\,\pi\,\,in^2)/(360^o) =(sector)/(165^o) \\ sector=(64\,\pi\,165^o)/(360^o)\,\,in^2\\sector\approx 92.15\,\,in^2`

Therefore, the area of the sector can be rounded to
`92.2\,\,in^2`