Answer:
[tex]\large\boxe{D)\ \dfrac{1}{2}\pi\ feet}[/tex]
Step-by-step explanation:
Step 1:
Calculate the circumference of both circles.
The formula of a circumference:of a circle with radius r:
[tex]C=2\pi r[/tex]
The circle R:
[tex]C_R=2\pi\left(\dfrac{2}{3}\right)=\dfrac{4\pi}{3}\ ft[/tex]
The circle S:
[tex]C_S=2\pi\left(\dfrac{3}{4}\right)=\dfrac{3\pi}{2}\ ft[/tex]
The length of the intercepted arc for circle R is
[tex]l=\dfrac{4\pi}{9}\ ft[/tex]
Step 2:
Calculate what the part of the circumference of the circle R is the intercepted arc:
[tex]\dfrac{4\pi}{9}:\dfrac{4\pi}{3}=\dfrac{4\pi}{9}\cdot\dfrac{3}{4\pi}=\dfrac{1}{3}[/tex]
The same length of the circumference of the circle S is searched for the length of the intercepted arc for circle S.
Step 3:
Calculate the length of the intercepted arc for circle S:
[tex]\dfrac{1}{3}\cdot\dfrac{3\pi}{2}=\dfrac{1}{2}\pi\ ft[/tex]
