Question

Can I get help with this problem?

Answer 1

Answer:

area of sector:

$\frac{theta}{360} \times \pi \: {r}^{2}$

$\frac{165}{360} \times \frac{22}{7} ( {8}^{2} )$

$\frac{11}{24} \times \frac{1408}{7}$

$\frac{1936}{21}$

$92.19 \: {in}^{2}$

Answer 2

Answer:

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

Step-by-step 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:

$\frac{64\,\pi\,\,in^2}{360^o} =\frac{sector}{165^o} \\ sector=\frac{64\,\pi\,165^o}{360^o}\,\,in^2\\sector\approx 92.15\,\,in^2$

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