Answer:
The correct option is C.
Step-by-step explanation:
Let the radius of circle B be x.
It is given that circles A and B have a central angle measuring 100°. The length of the intercepted arc for circle A is [tex]\frac{35}{9}\pi[/tex] meters and for circle B is [tex]\frac{25}{3}\pi[/tex] meters.
The formula of length of arc is
[tex]l=r\theta[/tex]
[tex]\theta =\frac{l}{r}[/tex]
Since central angel is same for both angles, therefore
[tex]\frac{l_1}{r_1}=\frac{l_2}{r_2}[/tex]
[tex]\frac{\frac{35}{9}\pi}{7}=\frac{\frac{25}{3}\pi}{x}[/tex]
[tex]\frac{35}{9\times 7}\pi={\frac{25}{3\times x}\pi[/tex]
[tex]\frac{5}{9}\pi=\frac{25}{3x}\pi[/tex]
[tex]x=\frac{25}{3}\times \frac{9}{5}=15[/tex]
The radius of circle B is 15 meters. Therefore the option C is correct.
