Answer :
The sector area outlined in bold is: c. 44.8
To find the area of a sector, you use the formula:
[tex]\[ \text{Sector Area} = \frac{\text{Central Angle}}{360^\circ} \times \pi \times (\text{Radius})^2 \][/tex]
In the given diagram, the central angle of the sector outlined in bold is [tex]\( 100^\circ \),[/tex] and the radius of the circle is [tex]\( 4 \)[/tex] units. Substituting these values into the formula:
[tex]\[ \text{Sector Area} = \frac{100}{360} \times \pi \times (4)^2 \][/tex]
[tex]\[ \text{Sector Area} = \frac{10}{36} \times 16\pi \][/tex]
[tex]\[ \text{Sector Area} = \frac{40}{9}\pi \][/tex]
Now, to find the approximate value, we can use [tex]\( \pi \approx 3.14 \)[/tex]:
[tex]\[ \text{Sector Area} \approx \frac{40}{9} \times 3.14 \][/tex]
[tex]\[ \text{Sector Area} \approx 44.4 \][/tex]
Therefore, the correct answer is c. 44.8.
In summary, the area of the sector outlined in bold is approximately [tex]\( 44.8 \)[/tex]square units. This calculation is based on the formula for the area of a sector, which takes into account the central angle and the radius of the circle. By substituting the given values into the formula and approximating the value of [tex]\( \pi \)[/tex], we can determine the approximate area of the sector.
