Answer:
C. [tex]\frac{9}{4}\pi\text{ ft}^{2}[/tex].
Step-by-step explanation:
We have been given that circles A and B have a central angle measuring 40°. Additionally, circle A has a radius of 5/2 ft and the radius of circle B is 9 /2 ft.
Let us find measure of the sector of circle B using sector area formula.
[tex]\text{Area of sector}=\frac{1}{2}\times\frac{\text{Central angle}}{180}\times \pi r^{2}[/tex]
Let us substitute our given values in sector area formula.
[tex]\text{Area of sector of circle B}=\frac{1}{2}\times\frac{40}{180}\times \pi\times (\frac{9}{2})^{2}[/tex]
[tex]\text{Area of sector of circle B}=\frac{40}{360}\times \pi\times \frac{81}{4}[/tex]
[tex]\text{Area of sector of circle B}=\frac{1}{9}\times \pi\times \frac{81}{4}[/tex]
[tex]\text{Area of sector of circle B}=\frac{9}{4}\pi[/tex]
Therefore, the area of sector for circle B will be [tex]\frac{9}{4}\pi\text{ ft}^{2}[/tex] and option C is the correct choice.
