Question

I don't understand how to answer this​

Answer 1

Answer:

$\large\boxe{D)\ \dfrac{1}{2}\pi\ feet}$

Step-by-step explanation:

Step 1:

Calculate the circumference of both circles.

The formula of a circumference:of a circle with radius r:

$C=2\pi r$

The circle R:

$C_R=2\pi\left(\dfrac{2}{3}\right)=\dfrac{4\pi}{3}\ ft$

The circle S:

$C_S=2\pi\left(\dfrac{3}{4}\right)=\dfrac{3\pi}{2}\ ft$

The length of the intercepted arc for circle R is

$l=\dfrac{4\pi}{9}\ ft$

Step 2:

Calculate what the part of the circumference of the circle R is the intercepted arc:

$\dfrac{4\pi}{9}:\dfrac{4\pi}{3}=\dfrac{4\pi}{9}\cdot\dfrac{3}{4\pi}=\dfrac{1}{3}$

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:

$\dfrac{1}{3}\cdot\dfrac{3\pi}{2}=\dfrac{1}{2}\pi\ ft$