Question

I don't understand how to answer this​

Answer 1

`\large\boxe{D)\ (1)/(2)\pi\ feet}`

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((2)/(3)\right)=(4\pi)/(3)\ ft`

The circle S:

`C_S=2\pi\left((3)/(4)\right)=(3\pi)/(2)\ ft`

The length of the intercepted arc for circle R is

`l=(4\pi)/(9)\ ft`

Step 2:

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

`(4\pi)/(9):(4\pi)/(3)=(4\pi)/(9)\cdot(3)/(4\pi)=(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:

`(1)/(3)\cdot(3\pi)/(2)=(1)/(2)\pi\ ft`